The elementary problem of a block sliding down an inclined plane is examined in detail with respect to different oriented coordinate systems that are typically not utilized due to the complexity of the problem. After solving for the equation of motion in these different coordinate systems group theory is applied and shown to yield the same results.
Secrest, Jeffery A. and Considine, Christopher Ryan
"Arbitrary Rotated Coordinate Systems for the Inclined Plane as an Introduction to Group Theory in the Introductory Physics Classroom,"
Georgia Journal of Science, Vol. 75, No. 2, Article 8.
Available at: https://digitalcommons.gaacademy.org/gjs/vol75/iss2/8