Lagrangian submanifolds and the Euler-Lagrange equations in higher-order mechanics |
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Authors: | M Crampin |
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Institution: | (1) Faculty of Mathematics, The Open University, Walton Hall, MK7 6AA Milton Keynes, U.K. |
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Abstract: | A direct construction of the Euler-Lagrange equations in higher-order mechanics as a submanifold of a higher-order tangent bundle is given, starting from the Lagrangian submanifold defined by the Lagrangian function. This construction uses higher-order tangent bundle geometry, derives the Euler-Lagrange equations as the constraint equations of a submanifold, and makes no assumptions about the regularity of the Lagrangian. |
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Keywords: | 58F05 70H35 58A20 |
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