Linear Algebra and Its Applications by Peter D. Lax

Author:Peter D. Lax
Language: eng
Format: epub
Publisher: Wiley
Published: 2013-05-15T16:00:00+00:00

therefore (8) can be written as

(10)

This shows that A(t) is antisymmetric. Equation (9) itself can be rewritten by multiplying by M on the right and using (1);

(11)

Note that if we differentiate (6) and use (11) we get the same equation

(11)1

This shows the significance of A(t), for the motion is independent of the reference time; A(t) is called the infinitesimal generator of the motion.

EXERCISE I. Show that if M(t) satisfies a differential equation of form (11), where A(t) is antisymmetric for each t and the initial condition (5), then M(t) is a rotation for every t.

EXERCISE 2. Suppose that A is independent of t; show that the solution of equation (11) satisfying the initial condition (5) is

(12)

EXERCISE 3. Show that when A depends on t, equation (11) is not solved by

Download

Copyright Disclaimer:
This site does not store any files on its server. We only index and link to content provided by other sites. Please contact the content providers to delete copyright contents if any and email us, we'll remove relevant links or contents immediately.