Stability Analysis of Systems with Periodic Coefficients: an Approximate Approach

The paper deals with an approximate method of stability analysis for second order linear systems with p<;riodiQcoefficients. The periodic functions are approximated during the first period of motion by a constant, a linear or a quadratic function of time such that the resulting approximate equations have known closed form solutions. The approximate equivalent equations are generated through an expansion of periodic coefficients into ultraspherical polynomials. The stability criteria is determined from the solution of approximate equivalent system and the generalized Floquet theory. The technique is quite general and does not require any restriction on the magnitudes of system parameters. In particular, the method has been applied to cOnstruct approximate stability chart for the Mathieu equation. A close agreement between the approximate and the exact result is found even for large values of system Parameters.