COMPLEX DYNAMICS SIMPLIFIED
1
COMPLEX DYNAMICS
SIMPLIFIED
To develop a control system for a dynamical
system one must first understand precisely how the
system
behaves.
One
can
arrive
at
this
understanding using mathematics by performing a
dynamic analysis. Dynamic analysis is performed
in two steps, often called the formulation or the
modeling step and the second simply called the
solution step. In the formulation step the equations
that describe the system are developed. In the
solution step, the equations are solved. One often
distinguishes between solutions that are obtained
analytically
and
those
that
are
obtained
numerically. The equations, when solving them
analytically, are often approximated by constant-
coefficient linear differential equations, because
they can be solved analytically with relative ease.
When solving the equations analytically, quantities
like
displacement,
velocity,
and
force
are
expressed
as
algebraic
functions
of
time.
Displacements, velocities and forces are called
time responses. The other way to solve the original
equations, the numerical approach, produces time
responses in the form of computer graphs.
MAE 461:
DYNAMICS AND CONTROLS

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