Thesis - Leigh Moody.pdf - Bad Request - Cranfield University

Appendix D / Point Mass Dynamics
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APPENDIX D
17 POINT MASS DYNAMICS
Appendices A to C provide a framework for defining the position of points,
and the transformation of the forces and moments acting on them, that
produce changes in their linear and angular velocity, acceleration and jerk.
Some commonly used dynamical relationships are revisited and expressed in
terms of the globally applied nomenclature. The approach is purposely
generic since these dynamics occur in many aspects of the work concerning
the absolute motion of the launcher, missile and target, and the relative
motion between each. The presentation of the relationships using the global
nomenclature provides insight to the terms that appear when developing
conventional missile guidance laws, and when using trajectory optimisation.
To avoid confusion with specific frames and vectors, two general axis
systems "I" and "R" are used. "I" represents a stationary reference frame
located at point (a) and "R" a general set of rotating axes located at a
different point (b) as shown in Figure 17-1.
The relationship between Euler triplets and body rates is explored first,
followed by transformation matrix time derivatives, and the extraction of
average angular rates from the evolution of direction cosines. These
relationships are key when deriving the velocity, acceleration and jerk of a
point, and their reduced forms when the Euler roll angle is ignored.
17-1