Abstract
This paper focuses on Gauss principle of least compulsion for relative motion dynamics and derives differential equations of motion from it.Firstly,starting from the dynamic equation of the relative motion of particles,we give the Gauss principle of relative mo-tion dynamics.By constructing a compulsion function of relative motion,we prove that at any instant,its real motion minimizes the com-pulsion function under Gaussian variation,compared with the possible motions with the same configuration and velocity but different ac-celerations.Secondly,the formula of acceleration energy and the formula of compulsion function for relative motion are derived because the carried body is rigid and moving in a plane.Thirdly,the Gauss principle we obtained is expressed as Appell,Lagrange,and Nielsen forms in generalized coordinates.Utilizing Gauss principle,the dynamical equations of relative motion are established.Finally,two rela-tive motion examples also verify the results'correctness.
基金项目
National Natural Science Foundation of China(12272248)
National Natural Science Foundation of China(11972241)
NETL
NSTL
万方数据