# Canonical Transformation

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.

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.