Separability of time-dependent second-order equations
A theory is developed concerning the geometric characterization of separable systems of second-order ordinary differential equations. The idea is to find necessary and sufficient conditions which will guarantee the existence of coordinates, with respect to which a given system decouples. The methodology stems from the theory of derivations of scalar and vector-valued forms along the projection π0 1 : J1π → E, where E is fibred over R (projection π). Particular attention is paid to features of the time-dependent set-up, which differ from the previously developed theory for autonomous equations.
KeywordsVector Field Tensor Field Linear Connection Horizontal Lift Autonomous Equation
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