# Change of Coordinates Lagrangian

Consider a Lagrangian system, with configuration space R^n, given by (x^1, ... x^n); and Lagrangian L(x', ..., x^n; v^1, ... v^n). Now consider a new system of coordinates, (y^1,... ^n), for this same system, so the y's are functions of the x's; and, inverting, the x's are also functions of the y's. Find the Lagrangian in the y-coordinate system, and show that it produces the same physical equations of motion for the system as does the Lagrangian in the x-coordinate system.

Â© BrainMass Inc. brainmass.com March 4, 2021, 6:11 pm ad1c9bdddfhttps://brainmass.com/math/derivatives/change-coordinates-lagrangian-33415

#### Solution Preview

Please see attachments for complete solution.

We use the general formulas of multivariate calculus and the ...

#### Solution Summary

The solution is attached below in two files. The files are identical in content, only differ in format. The first is in MS Word XP Format, while the other is in Adobe pdf format. Therefore you can choose the format that is most suitable to you.