New Developments in Differential Geometry pp 363-371 | Cite as

# Separability of time-dependent second-order equations

## Abstract

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 π^{0} _{1} : J^{1}π → *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.

## Keywords

Vector Field Tensor Field Linear Connection Horizontal Lift Autonomous Equation## Preview

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## References

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