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Grade: 12
        
Explain 20 applications of dynamics in engineering.
one month ago

Answers : (2)

Vikas TU
8721 Points
							
Dear student 
A 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
aswanth nayak
66 Points
							
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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