# Classical Mechanics Homework Solutions

You don't know if you can do this unless you actually do it.So don't say, "now I know" unless you have done it from start to stop on your own. Your solution should include the problem setup as well as enough printed graphics you need to show that you have a working animation.Lecture 31: Mon Nov 11 (Guest lecturer: Matt Kelly) Notes corrected on 11/29/2013 Topics: Double pendulum Lecture 32: Wed Nov 13 (Guest lecture: Hod Lipson) Topics: Design automation of kinematic and dynamical systems Lecture 33: Fri Nov 15 (Guest lecture: Mark Psiaki) Topics: Inverted-pendulum tight-rope walker with a balance beam.

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2) Use of Angular Momentum balance to get equations of motion for complex systems. Position, velocity and acceleration in cartesian and polar coordinates. Taylor Ch 1 Associated homeworks: (due Wed Sept 4, see HW policy): 1) Taylor 1.17b (use the definition of derivative) 2) Taylor 1.23 3) Taylor 1.45 4) 1D, no friction, no gravity. In principle you should be able to do almost all of them. Lecture 2: Fri Aug 30 (Guest lecturer: Anoop Grewal) Topics: Newtons laws and ballistics.

3) Mechanisms (linked rigid objects) 4) DAE f (Differential Algebraic Equations) formulation of equations of motion (Guest lectures on Aug 30, Oct 2, 25, Nov 11,13,15) If highlighted, notes are linked, courtesy of a student in the class. Reading: Taylor Ch 2.1-4, RP Ch 11.1-2 Associated homeworks: (due Wed Sept 11): 1) 2.12 2) 2.13 3) 2.21 4) 2.36 *** Labor Day, no class on Monday Sept 2*** Lecture 3: Wed Sept 4 Topics: and solution using Matlab with FEVAL (ODE solver in a separatefunction fom right-hand-side function).

Associated homeworks: (due Friday Oct 25 in class): 1) Write three matlab functions that solve the general spring-mass IVP (Initial Value Problem) a) [tarray xarray] = Springmass NUM(tspan, x0,v0, K, M) This can use ODE45 or your own ODE integrator, your choice.

It should work with arbitrary positive definite symmetric M and K matrices of any size.

b) Instead of using cosine and sine for the normal modes, use exponentials and do complex math to solve for the initial conditions. 6) A uniform hoop (a circular line) with mass m and radius R swings in the plane from a stationary frictionless pivot on the hoop at O.

## Comments Classical Mechanics Homework Solutions

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