New Developments in Differential Geometry pp 7785  Cite as
A linear connection associated with any second order differential equation field
Abstract
There are several problems concerning systems of secondorder ordinary differential equations
x= ^{ i }(t,x ^{ j } x^{ j })

is the system trivial, i.e. is there a change of coordinates y ^{ i } = y ^{ i } (t,x ^{ j } ) such that the system becomes ÿ^{i} = 0?

is the system linear, i.e. is there a change of coordinates which makes the righthand side linear in y^{i}

is the system separable, i.e. is there a change of coordinates such that the system separates into independent systems of lower dimension?

is the system derivable from a Lagrangian (the inverse problem of the calculus of variations)?
Keywords
Vector Field Vector Bundle Linear Connection Horizontal Structure Local TrivializationPreview
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References
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