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In many mechanics problems, the phase space is the cotangent bundle T*Q of a configuration space Q. There is an “intrinsic” symplectic structure on T*Q that can be described in various equivalent ways. Assume first that Q is n-dimensional, and pick local coordinates (q 1, ... ,q n ) on Q. Since (dq 1 , ... , dq n ) is a basis of T q * Q, we can write any α ∈ T q * Q as α = p i dq i This procedure defines induced local coordinates (q 1, ... , q n , p 1, ... , p n ) on T*Q.
KeywordsConfiguration Space Symplectic Form Symplectic Manifold Canonical Transformation Cotangent Bundle
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