Chapter 3
Computer Simulation of Dynamic
Systems
3.1 Dynamic System Modeling
A dynamic system is understood to mean any system, generally speaking, not only
mechanical, the state of which can change over time [1–7]. A dynamic system is
one of the most common mathematical models. This model arises when it becomes
necessary to describe the mechanical motion of bodies in space under the action of
applied forces. The position of the body is determined by its spatial coordinates,
which continuously change from the initial value to the final value in the observation
interval. The equations of the mathematical model describing the movement of the
body give rise to the trajectory of its movement.
One of the simplest examples of mechanical dynamical systems is a material point
capable of moving in three-dimensional space. The point state is set by six quantities.
Three of these quantities are the Cartesian coordinates x, y, z; the other three are the
corresponding components of the point velocity vector.
The time-dependent quantities that define the state of a dynamic system are called
state variables or dynamic variables. In a theoretical study of any dynamic system,
an operator is used, with the help of which they seek to find out how its state changes
over time. The form of the operator may be differential, integral, or some other.
Further, we will focus only on operators represented in differential form, that is,
dynamic systems will be considered, the behavior of which is determined by the
solutions of differential equations. The choice of the analytical description method
sets, as is customary to say, the mathematical model of a dynamic system.
A model of a dynamic system describes an object or process for which the concept
of a state is uniquely defined as a set of variables characterizing it at a given moment
in time, and a law is given that describes the change (evolution) of the initial state
over time. This law allows for the initial state to clearly predict the future state of a
dynamic system. This law is often called the law of system evolution.
© Springer Nature Singapore Pte Ltd. 2020
K. Rozhdestvensky et al., Computer Modeling and Simulation
of Dynamic Systems Using Wolfram SystemModeler,
https://doi.org/10.1007/978-981-15-2803-3_3
89
Computer Simulation of Dynamic
Systems
3.1 Dynamic System Modeling
A dynamic system is understood to mean any system, generally speaking, not only
mechanical, the state of which can change over time [1–7]. A dynamic system is
one of the most common mathematical models. This model arises when it becomes
necessary to describe the mechanical motion of bodies in space under the action of
applied forces. The position of the body is determined by its spatial coordinates,
which continuously change from the initial value to the final value in the observation
interval. The equations of the mathematical model describing the movement of the
body give rise to the trajectory of its movement.
One of the simplest examples of mechanical dynamical systems is a material point
capable of moving in three-dimensional space. The point state is set by six quantities.
Three of these quantities are the Cartesian coordinates x, y, z; the other three are the
corresponding components of the point velocity vector.
The time-dependent quantities that define the state of a dynamic system are called
state variables or dynamic variables. In a theoretical study of any dynamic system,
an operator is used, with the help of which they seek to find out how its state changes
over time. The form of the operator may be differential, integral, or some other.
Further, we will focus only on operators represented in differential form, that is,
dynamic systems will be considered, the behavior of which is determined by the
solutions of differential equations. The choice of the analytical description method
sets, as is customary to say, the mathematical model of a dynamic system.
A model of a dynamic system describes an object or process for which the concept
of a state is uniquely defined as a set of variables characterizing it at a given moment
in time, and a law is given that describes the change (evolution) of the initial state
over time. This law allows for the initial state to clearly predict the future state of a
dynamic system. This law is often called the law of system evolution.
© Springer Nature Singapore Pte Ltd. 2020
K. Rozhdestvensky et al., Computer Modeling and Simulation
of Dynamic Systems Using Wolfram SystemModeler,
https://doi.org/10.1007/978-981-15-2803-3_3
89