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Unformatted text preview: izes this inertia matrix. Does the resulting transformation make sense (relate it to the elements in the original inertia matrix)? (c) Given this diagonal inertia matrix, discuss the stability of the rotation of the rigid body about each of the principal axes. 2 3. A box of mass m o supports a simple pendulum of mass m and length l . A spring of stiﬀness forms a horizontal mass-spring system with the box which can slide without friction on a horizontal surface. (a) Use Lagrangian techniques to ﬁnd the diﬀerential equations of motion of the system. (b) What are the linearized equations, assuming that both x and θ are small? (c) Modify the Lagrangian in part (a) to include a damper c that acts in parallel with the spring. What are the new equations of motion? 3...
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- Spring '03
- inertia matrix, diagonal inertia matrix, original inertia matrix, horizontal turntable rotates