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PHYS350 - Summary

# Axis is semi minor axis is also called the impact

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Unformatted text preview: cular distance from a focus to the asymptote Note that and hence the lack of absolute values on compared to elliptical case Kinetic Energy: Relationship between impact parameter, initial velocity, and angle between asymptotes (scattering angle): Potential energy: Chapter 8: Many Body Systems: Equation of motion: Total energy: Internal conservative forces: Euler angles Three rotations are sufficient to rotate a body to its principal orientation 0. Start with 1. Rotate by angle about axis 2. Rotate by angle Lagrangia n: axis 3. Rotate by angle about axis Generalized coordinates of particles: Kinetic energy Rocket emitting matter at constant velocity u relative to rocket with speed v. For a symmetric body, last rotation is unnecessary Kinetic energy in terms of rate of change in Euler angles: Map coordinates: Rockets about Rotation with misalignm ent with principal axis: Chapter 9: Rigid Bodies Stable if Constraints or , in which case and 6 more degrees of freedom describes position of all particles takes 3 degrees of freedom (trivial for isolated system) Chapter 10: Lagrangian Mechanics Angular velocity, angular momentu m, and moment of inertia Most general case: Conservative force: Velocity-potential: Principal moments of inertia Principal axes: Kinetic energy: Most general force: Chapter 12: Hamiltonian mechanics Definition: Dissipative force: - Examples: Damped harmonic oscillator: Derivatives of : Charged particle in EM field: Natural system (not forced): Motion of a stretched string: Action integral: In general, To apply, just plug into definition and then make sure only depends on and ....
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