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achapt 1

# achapt 1 - COMPLEX DYNAMICS SIMPLIFIED 1 COMPLEX DYNAMICS...

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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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