By Sergio Pissanetzky
A contemporary, in-depth presentation of the speculation and rules of inflexible physique Kinematics at a College-level, with C++ resource code.
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Additional resources for Rigid Body Kinematics and C++ Code
The direction is defined by the line of the unit vector a. Axis w is the polar axis. 7. THE BODIES AND CONSTRAINTS GRAPH 29 perpendicular to the polar axis. 26. Singularities exist at β = 0 and β = π, since in this case au = av = 0 and α is undefined. There is also a singularity at au = 0, which is easy to deal with provided av = 0. To avoid the β singularities we use conventions. Let the unit vector a be defined in any coordinate system (x, y, z). The following procedure is used to define the conventions: Select the coordinate axis with the smallest absolute component of a as the polar axis, and rename it as w.
Articulations may exist that partially constrain the relative motion of the bodies. Many different coordinate systems need to be defined and used in the calculations. A global coordinate system C++, assumed to be inertial, a system attached to each body with the origin at the center of mass and the axes parallel to the principal axes of inertia, a system at each point where an articulation is attached to describe 24 CHAPTER 2. GRAPHS AND COORDINATE SYSTEMS the relative motion and the constraining effects of the articulation.
When system S moves, it drags point P with it. 5. 1: Two coordinate systems, F(p, q, t) and S(u, v, w). A point P is also shown, at a fixed position rSP with reference to system S. When system S moves, it drags point P with it. • The symbol rSP designates a vector object, with the invariant attributes of direction and magnitude which do not change in a coordinate transformation. Note, however, that nothing has been said about the time dependence of rSP . In particular, if system S is rotating, rSP is a function of time and r˙ SP is not zero.
Rigid Body Kinematics and C++ Code by Sergio Pissanetzky