# p09fl23 - Lecture 23 Euler equations(26 Oct 09 A Review...

This preview shows pages 1–2. Sign up to view the full content.

Lecture 23: Euler equations (26 Oct 09) A. Review: Euler’s equations 1. Calculate the time derivative of angular momentum relative to the center of mass in terms of torques d ~ L dt | inertial = d ~ L dt | body + × ~ L = ~ Γ 2. Take the body-ﬁxed axes to be the principal axes of the moment of inertia tensor (3 orthogonal vectors ˆ e ( s ) j , eigenvalues I j ), ~ L = I 1 ω 1 ˆ e 1 + ... , ˆ e 1 × ˆ e 2 = ˆ e 3 (and cyclic); t -derivative is in body frame. I 1 1 dt = ω 2 ω 3 ( I 2 - I 3 ) + Γ 1 3. Note that in this form the vector components are projected onto body- ﬁxed time-dependent axes, especially when there is a torque. The solu- tion for motion with external torques requires a self-consistent analysis. Discussion at end of Sec. 26: “body-associated” axes rather than body- ﬁxed axes arise in Problem 5.2. 4. then some examples from FW sec. 28. B. Compound pendulum 1. Rigid body constrained to rotate about a stationary ﬁxed axis ˆ e 3 . 2. Locate the center-of-mass (cm) in the plane perpendicular to ˆ

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 3

p09fl23 - Lecture 23 Euler equations(26 Oct 09 A Review...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online