Mentor
Oscar Varela
Document Type
Article
Publication Date
4-21-2020
First Page
1
Last Page
12
Abstract
By approaching Lagrangian mechanics from a graphical perspective the implications of Noether’s Theorem can be made easier to understand. Plotting the Lagrangian for classical single particle systems for one coordinate onto a position-velocity phase space along with the corresponding equations of motion can demonstrate how a system is invariant under continuous transforms in that coordinate. This invariance can be shown to be associated with a quantity in the system that’s conserved via Noether’s Theorem. The relationship between the symmetry of the system and conserved quantities can then be extended to fields. Invariance in this case is extended to include invariance under any continuous transform in the time, space, and field variables.
Recommended Citation
Moser, Seth, "Understanding Noether’s Theorem by Visualizing the Lagrangian" (2020). Physics Capstone Projects. Paper 86.
https://digitalcommons.usu.edu/phys_capstoneproject/86