Aladjev
V.Z., Bogdevicius M.A.
Interactive Maple:
Programming, Solution of Mathematical, Statistical, Engineering
and
Physical Problems.
2nd ed.- Tallinn - Vilnius:
Vilnius
Gediminas Technical
University & International
Academy of Noosphere,
2002, ISBN 9985-9277-1-0
Summary
Table of Contents
Interactive
Maple: Programming, Solution of the Mathematical,
Statistical and Engineering-Physical Problems (Interactive Maple) is a HTML- and DOC-based
course for undergraduates or early postgraduates, as well as a reference book
for engineers and scientists who want to use the well-known computer algebra
system Maple in their professional activity.
During
1997 - 2002 we were intensively using the
mathematical package Maple
of releases 4,
5, 6, 7 and 8 both
with the purpose of exploration of its functional possibilities and solution in
its environment of different problems of mathematical nature. The results of
this work were thoroughly discussed in our seven books written in
Russian and published in Estonia, Lithuania, Russia and Byelorussia. The offered book is based on the
above-mentioned books on Maple-problematic
and concentrates on three main aspects of the package Maple, namely: (1)
major innovations of the most popular sixth release of the package and its application to the solution of
mathematical problems from the analysis, linear algebra and statistics (2), as well as physical and engineering problems (3).
The book consists of three parts: (1) New possibilities of the mathematical package Maple of the sixth release (Maple 6 hereinafter), (2) Applications of Maple
6 for the
solution of mathematical and statistical problems and (3) Applications of Maple
6 to the
solution of physical and engineering problems.
The first part contains quite extensive material
on important innovations of the package environment with respect to its
previous fifth release, whereas the two remaining
parts not only present the applied aspects of the package use for solution of
mathematical, statistical, physical and engineering problems, but also
introduce the reader a wide circle of functional facilities of the
package. The book contains a wide range of elaborated examples and exercises (with solutions) which are placed strategically throughout
the text for better understanding. Many of these examples present useful
procedures whose realization illustrates a whole series of effective recipes
and methods of programming, including non-standard ones.
Besides that, remarks and
recommendations about Maple of releases
5, 6 and 7 are
included in the book.
We consider them as
excellent additional information to become proficient in the offered material,
since many of them illuminate both the important features and some weak points
of the package. Many of them are valid even for the last eighth release of the package. We shall
present briefly the contents of separate chapters of the book.
The first chapter of the book represents the
basic information on the installation of Maple 6 and its file organization for the Windows-platform; next some problems of
optimized nature are considered, and finally, general information on the mode
of the parallel server of the package and its interfaces with known packages MatLab and Ms Excel 2000 is given. In the second chapter general information on the sixth release of Maple, including the elements of a common
structural organization of the package, questions of setting the values for
basic performances of its shell
(the user
graphical interface,
called Iris) and kernel are disclosed.
The sixth release of the package is strongly
emphasized since it is qualitative Rubicon between the previous and the
subsequent releases (7 and
8). Moreover, the sixth release among the subsequent releases
is being represented as the steadiest in operation on the Windows-platform which involves basic
innovations of the subsequent two releases. Much attention is devoted to the
question of compatibility of releases
6, 7 and 8 which
requires the most serious relation.
On the basis of two-level organization
of the package (the kernel - calculator and the shell - User Graphical Interface), the innovations of the work with the sixth release of the package in the
environment of its shell - external level of structural
organization of the package - are considered in detail in the third chapter,
which allows to work with a Maple-document
as a single whole. Careful attention is devoted to the expansion of the
facilities of the sixth release of the package with respect to
its fifth release, which had obtained a rather
wide dissemination as a powerful modern facility of computer algebra. The
information presented in the mentioned chapter allows the beginning of the
initial stage of the use of this release at the level of the functionalities of
its shell. In view of small principal
distinctions between the releases
6, 7 and 8, this
material can be useful for the users of the last releases of Maple as well.
The fourth chapter contains the detailed
information about the built-in programming language of Maple 6 with respect to its innovations. This
chapter gives information about all main innovations of the language, which
extend basic facilities of programming in the package environment. In fact,
there exist now the new programming features especially program modules, nested
lexical scopes, documentation features, object-oriented support, new plotting
features, etc. The programming environment of the sixth release with the illustration of all
its main elements and receptions of programming, including a lot
non-conventional ones, are discussed in detail. What is more, the chapter
presents both the basic tools of programming and the extended ones, which allow
the most experienced user to effectively program rather complex mathematical
problems from various appendices in the package environment.
The fifth chapter provides the examples of the
application of the package for the calculus problem solving. Here the following
problems of analysis are considered: calculation of equation radicals, solution
of equation and inequalities systems; theory of limits and functions
differentiation; algebraic and numerical integration of functions; work with
numeric and formal power series; solution of ordinary and partial differential
equations, etc. A new interesting technique for the programming of problems of
such type allowed by the sixth release is described.
The sixth chapter contains the examples of the
application of the package for problem solving of the linear algebra. Here the
basic problems from the following sections are considered: polynomial and
vector-matrix algebra, special representations of matrixes and systems of
linear equations as well as facilities of support of algebraic rules of
substitutions for various symbolic transformations and calculations, etc.
Special attention is paid to a new module Linear Algebra of linear algebra that is based on
highly effective algorithms of the NAG which is the leader in development of
software of such type in the world. The implantation into the sixth release of the package of the given
module has essentially strengthened the sphere of applications of the package
for numerical calculations. A new interesting technique of programming of
problems of linear algebra permitted by the sixth release of the package is considered in
this chapter.
The material of the fifth and sixth chapters is illustrated by a number of
examples, which introduce the sphere of standard and non-conventional
programming of mathematical problems in Maple 6 and its last seventh release. In the presented discussion,
the problems of these two chapters cover a basic course of higher mathematics
at universities and colleges of physical and engineering profile that can serve
as a good computer-based practice in a number of basic sections of higher
mathematics.
In the seventh chapter the tools of Maple
6 for the
statistical analysis of data are introduced. The consideration of statistical
tools of the package is being forestalled by the arguing for the main
prerequisites of the use of computer technology in the statistical analysis and
a brief survey of modern statistical software. Both built-in and modular tools
of the package for support of the statistical analysis are considered in
detail. The presentation is illustrated with examples, among which the original
procedures dilating statistical tools of the package and illustrating both the
standard and the non-conventional techniques of programming of problems of such
type occur.
From the eighth chapter the book represents the applied
aspects of Maple 6 with examples of solution of a great
deal of physical and engineering problems from such fields as classical
mechanics, hydrodynamics, hydromechanics, thermal conduction, elasticity
theory, etc. Each problem is represented in the following context: (1) general theoretical part (setting
of a problem), (2) initial data for solution of the problem, (3) brief description of Maple-program which solves the problem, and (4) test example of application of the given program for
solution of concrete application with the interpretation of the obtained
results. In addition, the source texts of the debugged Maple programs with the initial data for test
examples, which are appropriated to those programs, are represented on the CD-ROM with this book. The similar
organization of the material allows the reader to apply immediately in his/her
own professional activity the software considered in the book.
The presented programs can serve as both
the final software product and relevant material illustrating main functionalities
of the package. The material in the third part of the book is based on our
previous books, and the outcomes of adapting physical and engineering problems
are considered relative to the sixth release of the package. However, these Maple programs can run with any of the last
five releases of Maple, namely
5, 6,
7, 8 and
9.
Algorithms of physical and engineering
problems of the third part mainly use the finite
element method.
Actually, this is an essential tool for undergraduates or early postgraduates,
as well as a reference book for engineers and scientists who want to develop
quickly finite-element programs or implant their own Fortran programs into computer algebra system Maple. The finite element method adapted for
environment of Maple-language of the package appears to be
an interesting one. Let us study the contents of the last eight chapters of the book that compose its
third part of Maple appendices.
The eighth chapter of the book considers questions
of a computer solution in Maple 6 of basic problems of thermal
conductivity
having important value to solve many applied problems of thermal physics as
well as a combination of problems in the theory of elasticity and plasticity.
The solution in the package environment for the following problems is
considered to be: linear (1)
and non-linear (2) stationary problems of thermal
conductivity as well as linear (3)
and non-linear (4) non-stationary problems of thermal
conductivity. In particular, linear non-stationary heat conductivity equation
is one of the main equations describing convective heat exchange and mass
exchange occurring in the systems of various physical natures. Whereas the last
problem keeps not only the great independent value for definition of
non-stationary temperature fields in various matters and materials, but it is
also an important component of more complex physical and engineering problems
having rather wide fields of appendices as well.
In the ninth chapter the four problems of linear
mechanics of deformable bodies are considered. The main relations concerning the description of
tensely deformable state and the relations for resilient bodies are
established. Each problem is solved by the finite element method. The main
principles of solution of the next practically important problems are
presented: (1) the definition of geometrical
parameters of cross-sections of bodies, (2)
the calculation of rod constructions at static loads, (3) the plane problem of the theory of elasticity, and (4) the contact problem of two elastic bodies. The indicated
problems represent the applied interest; therefore Maple programs corresponding to them for a
number of the appendices are taken into consideration.
In the tenth chapter the dynamic
problems of the theory of elasticity representing major practical interest in designing the
objects of mechanical engineering are considered. The main problems here are:
the definition of own and forced oscillations of elastic bodies as well as the
research of the behavior of elastic systems at short-term loads. The problems
considered in the chapter generate the practical interest for the research of
the indicated questions. The main principles of solution of the other
practically important problems are represented: (1) research of our own and forced oscillations of the linear
rod systems, (2) the plane problem of the theory of
elasticity at dynamical loads, (3) a
dynamical problem of shells of arbitrary configuration, and (4) a geometrically non-linear problem of the theory of
elasticity at dynamical loads.
In the eleventh chapter the five
problems of hydrodynamics having the important applied value and allowing to solve many
engineering problems which are linked with the flow around bodies, oscillations
of constructions in a liquid, a percussion impulse action onto a liquid, etc.
are considered. The following problems are represented: an vortex-free motion
of a liquid in terms of potential of speeds (1), the flow function (2),
the Navier-Stokes equations describing common movement of a liquid (3), a solution of the Navier-Stokes equations in the terms of a vortical
function of the flow (4), widely used in the applied problems
of hydromechanics, and (5) a
non-stationary movement of a compressed liquid described by the potential of
speeds.
In the twelfth chapter the following problems of hydromechanics
which play an
important role in the research of problems are considered: (1) hydrodynamic lubrication between movable surfaces, (2) models of movement of the non-Newtonian liquid, (3) the problem of convective heat exchange and mass transfer
for an incompressible liquid, (4) a
model of convective heat exchange in a liquid, and (5) the models of movement of a liquid in hydraulic system.
All these problems play the important role in many technical appendices, of
hydro-mechanical nature above all.
When solving dynamic problems of solid
mechanics there is a necessity of the definition of moments
of inertia of masses of bodies of complex geometrical forms as well as systems of bodies with
respect to various axes of coordinates. For example, the thirteenth chapter considers the problems of the
definition of moments of inertia of masses of bodies with complex geometrical
forms and systems of such bodies. By tools of Maple
6 the following
interesting problems are studied: (1)
the calculation of moments of inertia of a solid; (2) the calculation of moments of inertia of the system of
solids; (3) the non-linear oscillations of
mechanical systems; (4) the derivation and solution of
equations of motion of a mechanical system with concentrated parameters, and (5) the calculation of transitional torsion oscillations in
a mechanical transmission.
The problems of moving
of transport along the uneven way are of great interest. When the transport moves along the
uneven way upon elements of its hanger bracket a rather large loads affect,
which in turn, decrease longevity of elements of hanger bracket and all carrier
as a whole, and also essentially influence onto its comfortable quality. In
this connection the fourteenth chapter of the book considers the
following interesting problems: (1)
movements of a carrier on an uneven way; (2)
the stationary random oscillations of a carrier; (3) movements of a car on an uneven railway path; (4) dynamics of pneumatic vibration extinguisher with steady
magnets, and (5) models of moving gas in a pneumatic
system.
Finally, the fifteenth chapter is devoted to the application
of the Maple 6 for solution of optimization problems.
In this chapter the problem of minimizing function of real variables under the
assumption that no constraint is imposed on the values of these variables is
considered in the light of different standpoints.
The material represented in the book
contains practically all innovations of the package and can serve as a basis of
usage of Maple 6 by a rather wide circles of the experts
from various fields, above all, dealing with the problems of the brightly
expressed mathematical nature. Orientation and organization of the book will
supplement the already available English literature on the given problems,
technical documents on the package including. It will be pointed out that the
book is illustrated by a whole series of rather interesting examples and
procedures containing a series of effective and non-conventional recipes of
programming in the environment of Maple 6/7/8/9 which represent an undoubted practical
interest.
The CD-ROM together with the book contains the
files with the source codes of Maple programs of the applied physical and
engineering problems and other examples considered in the book and also the Maple-procedures that are oriented onto a
number of appendices and extend the basic possibilities of
Maple of the last four releases.
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Table of Contents:
Part
1.
New possibilities of the mathematical package Maple
of the sixth release
(Maple 6)
Chapter 1. The main information on installation of the package Maple 6
1.1. Questions of
installation of the mathematical package Maple 6
1.2. File organization
of the mathematical package Maple 6
1.3. Mode of the
parallel server, MatLab- and Excel-interface of the package
Chapter 2. The main information on the
mathematical package Maple 6
2.1. Common information
on the mathematical package Maple 6
2.2. Elements of
general structural organization of the package Maple 6
2.3. Setting of values
for basic characteristics of shell and kernel of the Maple 6
2.4. Portability of
the mathematical package Maple 6
Chapter 3. A work in the shell environment of the package Maple 6
3.1. Access to
files in the mode of the main menu of the package (Group File)
3.2. Help information
over the package Maple 6 (Group Help)
3.3. Editing of the current
Maple-document (Group Edit)
3.4. Control by the
mode of visualization of components of the main window of the package and
current Maple-document (Group View)
3.5. Means of the
package for editing of text components of Maple-documents (Group Format)
3.6. Means of the
package for editing of current Maple-document by means of inserts (Group Insert)
3.7. Mechanism of
spreadsheets of the package Maple 6 (Group Spreadsheet)
3.8. Redefinition of
main parameters of the package Maple 6 (Group Options)
3.9. System of graphics menus of the package
shell Maple
6
Chapter 4. Main innovations of the programming language of the
package Maple
6
4.1. Changes of common character
of the Maple-language of the sixth release of the
package
4.2. Main changes of
internal modules of the mathematical package Maple 6
4.3. New
possibilities of plot means of the mathematical package Maple 6
4.4. New means of
the Maple-language for testing of data types and
data structures
4.5. Elements of
object-oriented programming in the environment of the Maple-language
4.5.1. Organization
of program modules of the Maple-language of the package
4.5.2. Organization of
package modules on the basis of programme modules
4.5.3. Organization
of package modules of hierarchical structure
4.5.4. Means of expansion of the modular
programming
4.5.5. Program
modules as a means of programming of objects
4.5.6. Parametric
programming on the basis of program modules
4.5.7.
Development of means of debugging of procedures and program modules
4.6. New control
means by numerical calculations of the Maple-language
4.7. New means of
the Maple-language for control of numerical
calculations
4.8. Some other
innovations of the built-in language of the package Maple 6
4.9. User libraries of procedures and
functions
Part 2.
Application of the package Maple 6
for solution of the mathematical and
statistical problems
Chapter 5. Elements of analysis in the environment of the package Maple 6
5.1. Calculation of the
equations radicals, solution of sets of equations and inequalities
5.2. Theory of limits,
special and singular points of expressions
5.3. Differential
calculus in the environment of the package Maple 6
5.4. Facilities for
algebraic and numerical integration of functions
5.5. Facilities of
operations with numerical and formal power series
5.6. Means of solution
of minimax problems in the package environment Maple 6
5.7. Facilities of the
package Maple
6 for fitting
and interpolation of functions
5.8. Solution of the
ordinary differential equations and their systems
5.9. Package facilities
for solution of partial differential equations
5.10. Educational
facilities of solution of the ordinary differential equations and their
systems
Chapter
6. Elements of higher algebra in the package environment Maple 6
6.1.
Facilities of polynomial algebra in the package environment Maple 6
6.2. Basic facilities of
linear algebra on the basis of the package linalg-module
6.3. Facilities of the linalg-module for special representations of
matrixes
6.4. Solution of sets
of the linear equations by facilities of the linalg-module
6.5. Means of linear
algebra in the environment of the LinearAlgebra-module of the package Maple 6
6.6. Algebraic rules of substitutions of
symbolic calculations
6.7. The package facilities for support of
data structures of type 'stack' and 'queue'
Chapter 7. Computing facilities of the package Maple 6 for statistical data analysis
7.1. Basic
prerequisites of usage of computer technology in statistics
7.2. A brief survey of statistical
software
7.3. Usage of the
class of PCs in the statistical analysis
7.4. Facilities of statistical analysis
in environment of the package Maple 6
7.5. Facilities of
statistical analysis of the module `stats` of the package Maple 6
7.5.1. Functions of a data analysis (submodule describe)
7.5.2. Smoothing of
the statistical data (submodule fit)
7.5.3. Numerical
evaluation of distributions (submodule statevalf)
7.5.4. Data
manipulation functions (submodule transform)
7.5.5. Generation of
pseudorandom numbers according to given distributions (submodule random)
7.5.6. Elements of
analysis of variance (submodule anova)
7.5.7. Facilities of
creation of the statistical graphs (submodule statplots)
7.6. Additional facilities of statistical
analysis in the environment of the package Maple 6
Part 3. Application of the Maple 6
for solution of engineering and physical
problems
Chapter 8. The base problems of a thermal conduction
8.1. Linear
stationary problem of a thermal conduction
8.1.1. Calculated
equations of a linear stationary process of heat exchange
8.1.2. Input data for
the solution of the problem
8.1.3. Brief
description of the Heat_st_linear program solving the problem
8.1.4. An example of
use of the Maple-program Heat_st_linear
8.2. Nonlinear
stationary problem of a thermal conduction
8.2.1. Calculated
equations of a nonlinear stationary process of heat exchange
8.2.2. Input data for
the solution of the problem
8.2.3. Brief
description of the Heat_st_nonlinear program solving the problem
8.2.4. An example of
use of the Maple-program Heat_st_nonlinear
8.3. Linear
non-stationary problem of a thermal conduction
8.3.1. Calculated
equations of a linear non-stationary process of heat exchange
8.3.2. Input data for
the solution of the problem
8.3.3. Brief
description of the Heat_nonst_linear program solving the problem
8.3.4. An example of
use of the Maple-program Heat_nonst_linear
8.4. Nonlinear
non-stationary problem of a thermal conduction
8.4.1. Calculated
equations of nonlinear non-stationary process of heat exchange
8.4.2. Input data for
the solution of the problem
8.4.3. Brief
description of the Heat_nonst_nonlinear program solving the problem
8.4.4. An example of
use of the Maple-program Heat_nonst_nonlinear
Chapter 9. Basic problems of the resiliency theory
9.1. Definition of
the geometrical characteristics of flat sections
9.1.1. Calculated expressions
for definition of the geometrical characteristics of flat sections
9.1.2. Input data for
the solution of the problem
9.1.3. Brief
description of the Geometry program solving the problem
9.1.4. An example of
use of the Maple-program Geometry
9.2. Computer-based
calculation of the rod systems
9.2.1. Calculated
equations of the rod systems
9.2.2. Input data for
the solution of the problem
9.2.3. Brief
description of the Strypas program solving the problem
9.2.4. An example of
use of the Maple-program Strypas
9.3. Plane problem
of the elasticity theory
9.3.1. The calculated equations
of a plane problem of the elasticity theory
9.3.2. Input data for
the solution of the problem
9.3.3. Brief
description of the Plane program solving the problem
9.3.4. An example of
use of the Maple-program Plane
9.4. Problem of contact of the elastic
bodies
9.4.1. The
calculated equations of the problem of contact of elastic bodies
9.4.2. Input data for
the solution of the problem
9.4.3. Brief
description of the Contact program solving the problem
9.4.4. An example of
use of the Maple-program Contact
Chapter 10. Dynamic problems of the elasticity
theory
10.1. Dynamic
problem of the rod systems
10.1.1. The calculated
equations of the rod systems dynamics
10.1.2. Input data for
the solution of the problem
10.1.3. Brief
description of the Dynamic_strypas program solving the problem
10.1.4. An example of
use of the Maple-program Dynamic_strypas
10.2. The plane problem
of the elasticity theory at dynamic loads
10.2.1. The calculated
equations of the elasticity theory problem at dynamic loads
10.2.2. Input data for
the solution of the problem
10.2.3. Brief
description of the Dynamic_plane program solving the problem
10.2.4. An example of
use of the Maple-program Dynamic_plane
10.3. Dynamic problem
of shells of an arbitrary contour
10.3.1. The calculated
equations of a problem of the shells
10.3.2. Input data for
the solution of the problem
10.3.3. Brief
description of the Dynamic_shell program solving the problem
10.3.4. An example of
use of the Maple-program Dynamic_shell
10.4. Geometrically
nonlinear problem of the elasticity theory at dynamic loadings
10.4.1. The calculated
equations of the nonlinear problem
10.4.2. Input data for
the solution of the problem
10.4.3. Brief
description of the Dynamic_body program solving the problem
10.4.4. An example of
use of the Maple-program Dynamic_body
Chapter 11. Basic hydromechanics problems
11.1. Nonvortical
motion of fluids, described by potential of velocities
11.1.1. The calculated
equations for potential motion of a fluid
11.1.2. Input data for
the solution of the problem
11.1.3. Brief
description of the Pot_flow program solving the problem
11.1.4. An example of
use of the Maple-program Pot_flow
11.2. Nonvortical
motion of a fluid, described by the stream function
11.2.1. The calculated
equations for motion of a fluid as the stream function
11.2.2. Input
data for the solution of the problem
11.2.3. Brief
description of the Stream_flow program solving the problem
11.2.4. An example of
use of the Maple-program Stream_flow
11.3. The Navier-Stokes's equations represented in the terms
of velocity-pressure
11.3.1. The calculated
equations of Navier-Stokes
11.3.2. Input data
for the solution of the problem
11.3.3. Brief
description of the Navier_Stokes program solving the problem
11.3.4. An example of
use of the Maple-program Navier_Stokes
11.4. Solution of
the Navier-Stokes's equations, written in the
terms of variables of the vortex and stream function
11.4.1. The
calculated equations of Navier-Stokes in variables of vortex and stream function
11.4.2. Input data for
the solution of the problem
11.4.3. Brief
description of the Vort_Stream program solving the problem
11.4.4. An example of
use of the Maple-program Vort_Stream
11.5. Non-stationary
motion of compressible fluid, described by potential of velocity
11.5.1. The calculated
equations of non-stationary potential motion of a fluid
11.5.2. Input data for
the solution of the problem
11.5.3. Brief
description of the Dpot_flow program solving the problem
11.5.4. An example of
use of the Maple-program Dpot_flow
Chapter
12. Some applied problems of hydromechanics
12.1. Equation of Reynolds for a stratum of lubrication
12.1.1. The calculated
equations of Reynolds
12.1.2. Input data for
the solution of the problem
12.1.3. Brief
description of the Reynold program solving the problem
12.1.4. An example of
use of the Maple-program Reynold
12.2. A model of
motion of a non-Newtonian fluid
12.2.1. The calculated
equations of motion of a non-Newtonian fluid
12.2.2. Input data for the solution of the problem
12.2.3. Brief
description of the NonNiuton program solving the problem
12.2.4. An example of
use of the Maple-program NonNiuton
12.3. A model of
convective heat exchange in a fluid
12.3.1. The calculated equations of
nonisothermal convective heat exchange
12.3.2. Input data for
the solution of the problem
12.3.3. Brief
description of the Heat_flow program solving the problem
12.3.4. An example of
use of the Maple-program Heat_flow
12.4. Problem of
heat exchange and mass transfer for an incompressible fluid
12.4.1. The calculated
equations of heat exchange and mass transfer
12.4.2. Input data for
the solution of the problem
12.4.3. Brief
description of the Heat_mass_flow program solving the problem
12.4.4. An example of
use of the Maple-program Heat_mass_flow
12.5. Models of
motion of a fluid in a hydraulic system
12.5.1. Motion
of a compressible fluid in a hydraulic system
12.5.2. Input data for
the solution of the problem
12.5.3. Brief
description of the Hydro program solving the problem
12.5.4. An example of
use of the Maple-program Hydro
Chapter 13. Applied problems of mechanics -
1
13.1. Calculation of
moments of inertia of a solid body
13.1.1. The calculated
expressions for definition of moments of inertia of a solid body
13.1.2. Input
data for the solution of the problem
13.1.3. Brief
description of the Mass_inertia program solving the problem
13.1.4. An example of
use of the Maple-program Mass_inertia
13.2. Calculation of
moments of inertia of a system of solid bodies
13.2.1. The calculated
expressions for determination of moments of inertia of a system of solid
bodies
13.2.2. Input data for
the solution of the problem
13.2.3. Brief
description of the Mass_system program solving the problem
13.2.4. An example of
use of the Maple-program Mass_system
13.3. Nonlinear
oscillations of mechanical systems
13.3.1. The calculated expressions
for description of nonlinear oscillations of mechanical systems
13.3.2. Input data for
the solution of the problem
13.3.3. Brief
description of the Amplitude program solving the problem
13.3.4. An example of
use of the Maple-program Amplitude
13.4. Derivation and
solution of equations of motion of a mechanical system with the concentrated
parameters
13.4.1. The calculated
expressions for deduction of equations of motion of a mechanical system
13.4.2. Input data for
the solution of the problem
13.4.3. Brief
description of the Pendium program solving the problem
13.4.4. An example of
use of the Maple-program Pendium
13.5. Calculation of
transition torsion oscillations in a mechanical transmission
13.5.1. The calculated
expressions for determination of torsional oscillations of mechanical
transmissions
13.5.2. Input data for
the solution of the problem
13.5.3. Brief
description of the Driver program solving the problem
13.5.4. An
example of use of the Maple-program Driver
Chapter 14. The applied problems of mechanics
- 2
14.1. Motion of a
carrier on a rough road
14.1.1. The calculated
expressions for definition of motion of a carrier
14.1.2. Input data for
the solution of the problem
14.1.3. Brief
description of the Trailer program solving the problem
14.1.4. An example of
use of the Maple-program Trailer
14.2. Stationary
casual oscillations of a carrier
14.2.1. The calculated
expressions for determination of motion of a carrier
14.2.2. Input
data for the solution of the problem
14.2.3. Brief
description of the Trailer_random program solving the problem
14.2.4. An example of
use of the Maple-program Trailer_random
14.3. Motion of a
carriage along a rough railway
14.3.1. The calculated
expressions for determination of a carriage motion
14.3.2. Input data for
the solution of the problem
14.3.3. Brief description
of the Carriage program solving the problem
14.3.4. An example of
use of the Maple-program Carriage
14.4. Dynamics of
pneumatic vibration-extinguisher with stationary magnets
14.4.1. Equation of a
vibration-extinguisher motion with stationary magnets
14.4.2. Input data for
the solution of the problem
14.4.3. Brief
description of the Damper program solving the problem
14.4.4. An example of
use of the Maple-program Damper
14.5. Models of gas
motion in a pneumatic system
14.5.1. Motion of gas
in a pneumatic system
14.5.2. Input data for
the solution of the problem
14.5.3. Brief
description of the Pneumo program solving the problem
14.5.4. An example of
use of the Maple-program Pneumo
Chapter 15.
Application of Maple
6 for solution of optimization
problems
15.1.1.1. Nelder and Mead’s method
15.1.1.2. Input data
for the solution of the problem
15.1.1.3. Brief
description of the Nelder_Mead program solving the problem
15.1.1.4. An example
of use of the Maple-program Nelder_Mead
15.1.2.1. Hooke and Jeeves’s method
15.1.2.2. Input data
for the solution of the problem
15.1.2.3. Brief
description of the Hooke_Jeeves program solving the optimization problem
15.1.2.4. An example
of use of the Maple-program Hooke_Jeeves
15.1.3.1. Davidon’s cubic interpolation method
15.1.3.2. Input data
for the solution of the problem
15.1.3.3. Brief
description of the Cubic_interpolation program solving the optimization problem
15.1.3.4. An example
of use of the Maple-program Cubic_interpolation
15.2. Gradient
methods for unconstrained optimization
15.2.1.2. Input data
for the solution of the problem
15.2.1.3. Brief description
of the Gradient program solving the problem
15.2.1.4. An example
of use of the Maple-program Gradient
15.2.2.1. Fletcher-Reeves and Polak-Ribiere method
15.2.2.2. Input data
for the solution of the problem
15.2.2.3. Brief
description of the Fletcher_Reeves_Polak_Ribiere program solving the problem
15.2.2.4. An example
of use of the Maple-program Fletcher_Reeves_Polak_Ribiere
15.2.3. Newton’s methods
15.2.3.2. Input data
for the solution of the problem
15.2.3.3. Brief
description of the Newtons_method program solving the optimization problem
15.2.3.4. An example
of use of the Maple-program Newtons_method
15.3. Quasi-Newton methods
15.3.1.2. Input data
for the solution of the problem
15.3.1.3. Brief
description of the QUASI_SIMPLE program solving the optimization problem
15.3.1.4. An example
of use of the Maple-program QUASI_SIMPLE
15.3.2. Davidon-Fletcher-Powell method
15.3.2.1. Algorithm of Davidon-Ftetcher-Powell method
15.3.2.2. Input data
for the solution of the problem
15.3.2.3. Brief
description of the Davidon_Fletcher_Powell program solving the problem
15.3.2.4. An example
of use of the Maple-program Davidon_Fletcher_Powell
15.3.3. Broyden-Fletcher-Goldfarb-Shanno method
15.3.3.1. Algorithm
of Broyden-Fletcher-Goldfarb-Shanno method
15.3.3.2. Input data
for the solution of the problem
15.3.3.3. Brief
description of the BFGS program solving the optimization problem
15.3.3.4. An example
of use of the Maple-program BFGS
15.3.4. Memoryless quasi-Newton method
15.3.4.1. Algorithm
of memoryless quasi-Newton method
15.3.4.2. Input data
for the solution of the problem
15.3.4.3. Brief
description of the Memoryless_QN program solving the optimization problem
15.3.4.4. An example
of use of the Maple-program Memoryless_QN
15.4. Constrained
minimization methods
15.4.1. Penalty-function
method
15.4.1.1. Fiacco and McCormick method
15.4.1.2. Input data
for the solution of the problem
15.4.1.3. Brief
description of the Fiacco_McCormick program solving the optimization problem
15.4.1.4. An example
of use of the Maple-program Fiacco_McCormick
15.4.2. Complex
method
15.4.2.1. Algorithm
of Complex method
15.4.2.2. Input data
for the solution of the problem
15.4.2.3. Brief
description of the Complex program solving the optimization problem
15.4.2.4. An example
of use of the Maple-program Complex
15.4.3. Methods
based on the sequence of linear programs. The first method
15.4.3.1. Cutting
plane method
15.4.3.2. Input data
for the solution of the problem
15.4.3.3. Brief
description of the Cutting_Plane program solving the optimization problem
15.4.3.4. An example
of use of the Maple-program Cutting_Plane
15.4.4. The method
based on the sequence of linear programs. The second method
15.4.4.1. Method of
approximate programming
15.4.4.2. Input data
for the solution of the problem
15.4.4.3. Brief
description of the SLP
program solving the optimization problem
15.4.4.4. An example
of use of the Maple-program SLP
15.5. Genetic
algorithms
15.5.1. The
procedure of genetic algorithm
15.5.2. Input data
for the solution of the problem
15.5.3. Brief
description of the Genetic_dalia program solving the optimization problem
15.5.4. An example
of use of the Maple-program Genetic_dalia
References
Appendixes
|
This monograph supplements the
already available literature on the Maple
package and its applied aspects with orientation towards the widest circle of
the Maple users dealing with physical and engineering
appendices.
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