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

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Summary

INTRODUCTION

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.

THE BELLMAN-GAUSS PRINCIPLE FOR CONSTRAINED MOTION
AN APPLICATION
DISCUSSION
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