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.
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The solution ...
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.