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This paper presents second-order switching time optimization techniques for nonlinear time-varying systems that are piecewise second-differentiable. The techniques are based on direct analysis of flows rather than constrained optimization methods, making it possible to take higher order derivatives. The resulting algorithms also use the same number of integrations along the trajectory regardless of the number of switching times. Two examples are included-a linear example seen previously in the literature and a nonlinear example that emphasizes the fast convergence rates of second-order optimizations compared to first order techniques (e.g. convergence in 19 iterations compared to over 25,000).