Theoretical Mechanics: Theoretical Physics 1 -

): 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.

ddt(𝜕L𝜕q̇i)−𝜕L𝜕qi=0d over d t end-fraction open paren the fraction with numerator partial cap L and denominator partial q dot sub i end-fraction close paren minus the fraction with numerator partial cap L and denominator partial q sub i end-fraction equals 0 Generalized Coordinates ( Theoretical Mechanics: Theoretical Physics 1

A set of three angles used to describe the orientation of a rigid body in 3D space. Study Strategy ): You can pick any coordinates (angles, distances)

A matrix describing how an object resists rotational motion. This motivates the next step

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 are swept out equally in time. 6. Rigid Body Dynamics Moving beyond point particles.