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PHYS350 - Summary

Single impulse at solution sum of impulse forces at

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Unformatted text preview: se at ; : Solution: Sum of impulse forces at time Trajectory (eliminate from above): - Arbitrary force (analogous to arbitrary periodic force above) Moments and angular momentum: We used this example quite a lot in our HW Torque: (Moment of a force about the origin) Angular momentum: (Moment of momentum about the origin) - Wasn’t really covered in class… see example on page 39. is first time at which force becomes non-zero Chapter 3: Energy and Angular Momentum Energy conservation in 3D Conservative force: Projectiles with no air drag: Equation of motion: Central forces: - Force is always parallel to position vector Cylindrical and spherical coordinates - Motion is confined to a plane Rate of area sweeping out by position vector is constant Split into components: Solution: Calculus of variations: Stationary values of an integral satisfy EulerLagrange equation: Maximum height, flight time, and range: In general Projectiles with air drag: Equation of motion: Split into components: Hamilton’s principle; Lagrange’s equation may depend on more things Lagrangian function in any coordinate system: Action integral: Inverse square law: Equations of motion: - Can be used to find the force in the which is Generalized momenta and forces (not necessarily the same as momentum and force): Chapter 4: Central Conservative Forces Isotropic harmonic oscillator Equation of motion: Energy conservati on: In g...
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