Approximation and Abstraction in Solid Object Kinematics
Ernest Davis · 1995
ion in Solid Object Kinematics Ernest Davis New York University 251 Mercer St. New York, New York [email protected] September 26, 1995 Abstract Physical reasoning often involves approximating or abstracting the situation or the theory at hand. This paper studies the nature of approximation and abstraction as applied to the kinematic theory of rigid solid objects. Five categories of approximation are considered: 1. Geometric approximation. 2. Abstraction of a complex kinematic structure by a simpler kinematic structure. For example, the abstraction of a collection of tightly-linked objects as a single object. 3. Abstraction of a kinematic structure by a simpler theory. For example, the abstraction by a connectivity graph in configuration space. 4. Approximation of a complex kinematic structure by more complex theory. For example, the approximation of a chain by a string. 5. Approximation of a more complex theory by a kinematic theory. For example, the approximation o...