Theoretical Mechanics: Theoretical Physics 1 Direct

Visualizing a system as a single point moving through a multidimensional space of . This is the bridge to Quantum Mechanics . 5. Central Force Motion The classic application of the tools above.

Reducing a two-body system (like Earth and Sun) to a one-body problem using Reduced Mass . Theoretical Mechanics: Theoretical Physics 1

Nature takes the path that minimizes the "Action" ( Euler-Lagrange Equation: Visualizing a system as a single point moving

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). Central Force Motion The classic application of the

q̇i=𝜕H𝜕pi,ṗi=−𝜕H𝜕qiq dot sub i equals the fraction with numerator partial cap H and denominator partial p sub i end-fraction comma space p dot sub i equals negative the fraction with numerator partial cap H and denominator partial q sub i end-fraction