Dynamic Response of Linear Mechanical Systems pp 85-231 | Cite as

# Time Response of First- and Second-order Dynamical Systems

## Abstract

How physical systems, e.g., aircraft, *respond* to a given input, such as a gust wind, under given initial conditions, like cruising altitude and cruising speed, is known as the*time response* of the system. Here, we have two major items that come into the picture when determining the time response, namely, the mathematical model of the system and the *history* of the input. The mathematical model, as studied in Chap. 1, is given as an ODE in the generalized coordinate of the system. Moreover, this equation is usually nonlinear, and hence, rather cumbersome to handle with the purpose of predicting how the system will respond under given initial conditions and a given input. However, if we first find the equilibrium states of the system, e.g., the altitude, the aircraft angle of attack, and cruising speed in our example above, and then linearize the model about this equilibrium state, then we can readily obtain the information sought, as described here.

### Keywords

Transportation Hull Convolution Sine Bide### References

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