Computational Physics by Philipp O. J. Scherer

Author:Philipp O. J. Scherer
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

14.9 Explicit Methods

Equation (14.61) for the rotation matrix and (14.62) for the angular momentum have to be solved by a suitable algorithm. The simplest integrator is the explicit Euler method (Fig. 14.3) [169]:

(14.67)

(14.68)

Expanding the Taylor series of A(t) to second order we have the second order approximation (Fig. 14.3)

(14.69)

A corresponding second order expression for the angular momentum involves the time derivative of the forces and is usually not practicable.

The time derivative of W can be expressed via the time derivative of the angular velocity which can be calculated as follows:

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