Simulation Center are described in detail. The third chapter gives a general idea
of the fundamental principles that underlie any mathematical model such as conservation laws or variational principles. On these principles, the simplest models are
built. These models are used as the basis for building more complex hierarchical
models. Application of fundamental principles is illustrated with examples such as a
harmonic oscillator. The reader gets acquainted with the hierarchical principle of
building models, from simple to complex. In the fourth chapter, the reader is invited
to study methods of modeling single component, multicomponent and hybrid
systems using two alternative approaches: developing computer models directly
with Modelica language and using component modeling technologies with application of the standard Modelica libraries. The following mechanical oscillatory
systems with one degree of freedom are considered: a mathematical pendulum, a
Galileo’s pendulum, an elastic pendulum. In the fifth chapter, the methods for
solving more complex problems are discussed. These are multicomponent and
hybrid systems. It is proposed to use two approaches: directly developing computer
models on the Modelica language and using component modeling technologies
with application of the standard Modelica libraries. The modeling of mechanical
oscillatory systems with several degrees of freedom is considered. The following
illustrative examples of such dynamic models are given: the relative motion of two
bodies, complex oscillatory mechanical systems of dampers and springs, and
coupled and double mathematical pendulums. The sixth chapter is devoted to
building hierarchical component models and creating custom libraries in the
Wolfram SystemModeler. The reader gets acquainted with the concepts of blocks
and connections. The concepts of oriented and non-oriented connections between
blocks are introduced. Mathematically, these connections include algebraic and
differential equations which describe the behaviors and interactions of system
objects. The following illustrative examples of such models are demonstrated:
model of draining of a tank; problem of heating a liquid mixture with the help of a
PID controller (by using the custom components); inverted pendulum problem.
viii
Reviewers
of the fundamental principles that underlie any mathematical model such as conservation laws or variational principles. On these principles, the simplest models are
built. These models are used as the basis for building more complex hierarchical
models. Application of fundamental principles is illustrated with examples such as a
harmonic oscillator. The reader gets acquainted with the hierarchical principle of
building models, from simple to complex. In the fourth chapter, the reader is invited
to study methods of modeling single component, multicomponent and hybrid
systems using two alternative approaches: developing computer models directly
with Modelica language and using component modeling technologies with application of the standard Modelica libraries. The following mechanical oscillatory
systems with one degree of freedom are considered: a mathematical pendulum, a
Galileo’s pendulum, an elastic pendulum. In the fifth chapter, the methods for
solving more complex problems are discussed. These are multicomponent and
hybrid systems. It is proposed to use two approaches: directly developing computer
models on the Modelica language and using component modeling technologies
with application of the standard Modelica libraries. The modeling of mechanical
oscillatory systems with several degrees of freedom is considered. The following
illustrative examples of such dynamic models are given: the relative motion of two
bodies, complex oscillatory mechanical systems of dampers and springs, and
coupled and double mathematical pendulums. The sixth chapter is devoted to
building hierarchical component models and creating custom libraries in the
Wolfram SystemModeler. The reader gets acquainted with the concepts of blocks
and connections. The concepts of oriented and non-oriented connections between
blocks are introduced. Mathematically, these connections include algebraic and
differential equations which describe the behaviors and interactions of system
objects. The following illustrative examples of such models are demonstrated:
model of draining of a tank; problem of heating a liquid mixture with the help of a
PID controller (by using the custom components); inverted pendulum problem.
viii
Reviewers