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Titlebook: Exterior Differential Systems and the Calculus of Variations; Phillip A. Griffiths Book 1983 Springer Science+Business Media New York 1983

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Euler Equations for Variational Problems in Homogeneous Spaces,It is well-known that a general curve γ⊂IE. has a Frenet frame.
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Endpoint Conditions; Jacobi Equations and the 2nd Variation; the Hamilton-Jacobi Equation,We consider a variational problem (I, ω; φ) with one independent variable on a manifold X.
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Preliminaries,the point p is T.(M), and the tangent bundle is .. We sometimes write points in T(M) as (p, v) where p∈M and v∈T.(M). A local coordinate system (x. ) on M induces a local coordinate system . on T(M) where p has coordinates (x.,...,x.) and .. ..
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Progress in Mathematicshttp://image.papertrans.cn/e/image/319872.jpg
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Exterior Differential Systems and the Calculus of Variations978-1-4615-8166-6Series ISSN 0743-1643 Series E-ISSN 2296-505X
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https://doi.org/10.1007/978-1-4615-8166-6Calculus of Variations; integral; manifold; variational problem
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