Nature takes the path that minimizes the "Action" ( Euler-Lagrange Equation:
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. Theoretical Mechanics: Theoretical Physics 1
A set of three angles used to describe the orientation of a rigid body in 3D space. Study Strategy Nature takes the path that minimizes the "Action"
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) 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
