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` Explain 20 applications of dynamics in engineering.`

one month ago

Dear studentA mathematical description of a dynamical system is

1. System of difference equations for the discrete case

2. Systems of differential equations for the continuous case

The revolution in digital technology has fueled a need for design techniques that can

guarantee safety and performance specifications of embedded systems, or systems that

couple discrete logics with analog physical environment. Such systems can be modeled by

hybrid systems, which are dynamical systems that combine continuous-time dynamics

modeled by differential equations and discrete-event dynamics modeled by finite

automata. Important applications of hybrid systems include CAD, real-time software,

robotics and automation, mechatronics, aeronautics, air and ground transportation

systems, process control etc. Recently, hybrid systems have been at the center of intense

research activity in the control theory, computer-aided verification, and artificial

intelligence communities, and methodologies have been developed to model hybrid

systems, to analyze their behaviors, and to synthesize controllers that guarantee closedloop safety and performance specifications.

Hybrid systems are dynamical systems that involve the interaction of different types of

dynamics. Hybrid dynamics provide a convenient framework for modeling systems in a

wide range of Engineering Applications :

a. In electrical circuits continuous phenomena such as the charging of capacitors are

interrupted by discrete phenomena such as by switching opening and closing, or diodes

going on or off.

b. In embedded computation systems a digital computer interacts with a mostly analog

environment

Nonlinear, chaotic systems can produce very irregular data; similar but distinct from a

stochastic system (i.e. system with probabilistic dynamics).

1. The rapid loss of predictability of chaotic systems is due to a phenomenon called

sensitive dependence on initial conditions.

2. For a certain class of dynamical systems, once transients are over, the trajectory of the

system approaches a subset of the state space called an attractor.

3. Attractors of dissipative chaotic systems generally are strange attractors-complicated

geometrical objects that exhibit fractal structure.

one month ago

Dear student,1. System of difference equations for the discrete case

2. Systems of differential equations for the continuous case

The revolution in digital technology has fueled a need for design techniques that can

guarantee safety and performance specifications of embedded systems, or systems that

couple discrete logics with analog physical environment. Such systems can be modeled by

hybrid systems, which are dynamical systems that combine continuous-time dynamics

modeled by differential equations and discrete-event dynamics modeled by finite

automata. Important applications of hybrid systems include CAD, real-time software,

robotics and automation, mechatronics, aeronautics, air and ground transportation

systems, process control etc. Recently, hybrid systems have been at the center of intense

research activity in the control theory, computer-aided verification, and artificial

intelligence communities, and methodologies have been developed to model hybrid

systems, to analyze their behaviors, and to synthesize controllers that guarantee closedloop safety and performance specifications.

Hybrid systems are dynamical systems that involve the interaction of different types of

dynamics. Hybrid dynamics provide a convenient framework for modeling systems in a

wide range of Engineering Applications :

a. In electrical circuits continuous phenomena such as the charging of capacitors are

interrupted by discrete phenomena such as by switching opening and closing, or diodes

going on or off.

b. In embedded computation systems a digital computer interacts with a mostly analog

environment

Nonlinear, chaotic systems can produce very irregular data; similar but distinct from a

stochastic system (i.e. system with probabilistic dynamics).

one month ago

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