Abstract
Gauss' principle of least constraint is solved in a sequential fashion via dynamic programming in this paper. The solution itself constitutes a new principle for constrained motion, which we may name the Bellman-Gauss principle for constrained motion.
Highlights
THE BELLMAN-GAUSS PRINCIPLE FOR CONSTRAINED MOTION Gauss' principle describes the relationship between the actual accelerations and the free motion accelerations
The algorithm derived from Bellman's principle of optimality gives an algorithm for converting a set of free motion accelerations to a set of actual accelerations
The Bellman-Gauss principle introduced in this paper provides new insights into the nature of constrained motion
Summary
Given initial conditions on x and x, such differentiations of the constraints do not produce any loss in generality In this case, Gauss' principle takes the form of minimizing G subject to the linear constraints (2). ··· + CkYk = dk is a consistent set of linear algebraic equations, dk is an m x 1 vector, and k = r, r + 1, ... The unique solution to the consistent set of linear algebraic equations Cry(r) = dr, in vector form, is. To find the shortest length solution to the consistent set of linear algebraic equations Cy = d, where C is a matrix with rank r whose first r columns are linearly independent, we may use the following {3 - R algorithm.
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