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    Canonical Transformation

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    The motion of an object of mass m in two dimensions, in the presence of a gravitational field may be determined from the Lagrangian: (look at attached for better formula representation)
    L = 1/2m (x^2+y^2) - mgy

    Consider the transformation give by:
    x' = x + alpha + beta(t)
    y' = y

    Where alpha and beta are constants. For this system:
    a. Show that the transformation is an invariance transformation by finding the function A
    b. Find the related infinitesimal invariance transformation and calculate sigma A
    c. Find the associated constants of the motion for two parameter transformations given above.

    © BrainMass Inc. brainmass.com June 4, 2020, 4:43 am ad1c9bdddf
    https://brainmass.com/physics/equilibrium/canonical-transformation-577594

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    Solution Summary

    The solution shows how to obtain the generating function of a canonical invariant transformation. It helps show that a transformation is an invariance transformation by finding a function, it finds the related infintesimal invariance transformation, and finds the associated constants of the motion for two parameter transformations.

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