1 Class #28 of 31 Inertia tensor Kinetic energy from inertia tensor. Eigenvalues w/ MATLAB Tops and Free bodies using Euler equations Precession Lamina.

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Presentation transcript:

1 Class #28 of 31 Inertia tensor Kinetic energy from inertia tensor. Eigenvalues w/ MATLAB Tops and Free bodies using Euler equations Precession Lamina theorem Free-body wobble :02

2 Rest of course :60 11/28THANKSGIVING 2812/3Tops, Gyros and Rotations#14 –Supplement / Taylor /5Ch. 13 Hamiltonian and Quantum Mechanics or Chaos 3012/10Test #4Inertia Tensor / Tops / Euler equations /Chaos 12/ /12Review for Final FINAL EXAM 12/16MONDAY – 9AM-12NOONWORKMAN 310

3 Angular Momentum and Kinetic Energy :02 We derived the moment of inertia tensor from the fundamental definitions of L, by working out the double cross-product Do the same for T (kinetic energy)

4 L 28-2 Angular Momentum and Kinetic Energy :02 1)A square plate of side L and mass M is rotated about a diagonal. 2)In the coordinate system with the origin at lower left corner of the square, the inertia tensor is.

5 Symmetrical top :02 Euler equation

6 Precession :02 Ignore in limit

7 Lamina Theorem :60

8 Euler’s equations for symmetrical bodies :60 Note even for non-laminar symmetrical tops AND even for

9 Euler’s equations for symmetrical bodies :60 Precession frequency=rotation frequency for symmetrical lamina

10 Euler’s equations for symmetrical bodies :60

11 L28-1 – Chandler Wobble :60 1)The earth is an ovoid thinner at the poles than the equator. 2)For a general ovoid, 3)For Earth, what are

12 L 28-2 Angular Momentum and Kinetic Energy :02 1)A square plate of side L and mass M is rotated about a diagonal. 2)In the coordinate system with the origin at lower left corner of the square, the inertia tensor is.

13 Lecture 28 windup :02

14 Angular Momentum and Kinetic Energy :02 1)A complex arbitrary system is subject to multi-axis rotation. 2)The inertia tensor is 3)A 3-axis rotation is applied