Deriving why orbits are ellipses and how areas are swept out equally in time. 6. Rigid Body Dynamics Moving beyond point particles.
): You can pick any coordinates (angles, distances) that suit the geometry, making complex systems much easier to solve. 3. Symmetry and Noether’s Theorem This is the "soul" of theoretical physics. Theoretical Mechanics: Theoretical Physics 1
Newtonian mechanics gets messy with "constraints" (e.g., a bead on a wire). This motivates the next step. 2. Lagrangian Mechanics (The Energy Approach) Instead of forces, we use Scalar Energy . The Lagrangian ( ): Defined as (Kinetic minus Potential energy). Deriving why orbits are ellipses and how areas
This reformulates mechanics to describe the "state" of a system using position ( ) and momentum ( Usually represents total energy, ): You can pick any coordinates (angles, distances)
For every continuous symmetry in the Lagrangian, there is a corresponding conservation law. Time Translation Symmetry →right arrow Conservation of Energy . Space Translation Symmetry →right arrow Conservation of Momentum . Rotation Symmetry →right arrow Conservation of Angular Momentum . 4. Hamiltonian Mechanics (The State Space)