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An extended Hamilton-Jacobi method. (English) Zbl 1328.70012
Summary: We develop a new method for solving Hamilton’s canonical equations. The method is based on the search for invariant vortex manifolds of special type. In the case of Lagrangian (potential) manifolds, we arrive at the classical Hamilton-Jacobi method.

MSC:
70H05 Hamilton’s equations
70H20 Hamilton-Jacobi equations in mechanics
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