Abstract A closed‐form solution of the variational equation associated with a piecewise‐linear differential equation is derived. This closed‐form solution is used to develop an efficient method for calculating the solution of the variational equation. The method relies on the matrix exponential and requires no integration beyond the calculation of the trajectory along which the variational equation is being solved. Numerical results for the three‐dimensional case show an increase in efficiency of one to two orders of magnitude over the traditional method.
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