高山滑雪运动是一项技术性很强的运动,滑雪板的特性直接影响着运动的效果,因此对滑雪板的研究有很大的现实意义.用数值研究的方法,从滑雪板的几何特性出发,在转弯半径关系式的基础上推导了滑雪板转弯运动时的约束方程,建立了单刚体人体...高山滑雪运动是一项技术性很强的运动,滑雪板的特性直接影响着运动的效果,因此对滑雪板的研究有很大的现实意义.用数值研究的方法,从滑雪板的几何特性出发,在转弯半径关系式的基础上推导了滑雪板转弯运动时的约束方程,建立了单刚体人体滑雪运动的广义L agrange-R ou th动力学方程,并对人体在平地和斜坡两种情况下的滑雪运动进行了数值仿真与分析.计算结果符合实际的实验结果,表明所建立的力学模型能较好地反映滑雪运动的力学特性,进而增强了对滑雪运动本质的理解,并为进一步的运动仿真提供必要的理论基础.展开更多
A nonlinear dynamic model of a simple nonholonomic system comprising a self-rotating cantilever beam subjected to a unilateral locked or unlocked constraint is established by employing the general Hamilton＇s Variatio...A nonlinear dynamic model of a simple nonholonomic system comprising a self-rotating cantilever beam subjected to a unilateral locked or unlocked constraint is established by employing the general Hamilton＇s Variational Principle. The critical values, at which the trivial equilibrium loses its stability or the unilateral constraint is activated or a saddle-node bifurcation occurs, and the equilibria are investigated by approximately analytical and numerical methods. The results indicate that both the buckled equilibria and the bifurcation mode of the beam are different depending on whether the distance of the clearance of unilateral constraint equals zero or not and whether the unilateral constraint is locked or not. The unidirectional snap-through phenomenon （i.e. catastrophe phenomenon） is destined to occur in the system no matter whether the constraint is lockable or not. The saddle-node bifurcation can occur only on the condition that the unilateral constraint is lockable and its clearance is nonzero. The results obtained by two methods are consistent.展开更多
In this paper the Lie-form invariance of the non-holonomic systems with unilateral constraints is studied. The definition and the criterion of the Lie-form invariance of the system are given. The generalized Hojman co...In this paper the Lie-form invariance of the non-holonomic systems with unilateral constraints is studied. The definition and the criterion of the Lie-form invariance of the system are given. The generalized Hojman conserved quantity and a new type of conserved quantity deduced from the Lie-form invariance are obtained. Finally, an example is presented to illustrate the application of the results.展开更多
This paper deals with the generalization of the fieldmethod to non-holonomic systems whose motion is subject toeither non-linear constraints or those of a higher order,whiletheir motion is modeled by the generalized L...This paper deals with the generalization of the fieldmethod to non-holonomic systems whose motion is subject toeither non-linear constraints or those of a higher order,whiletheir motion is modeled by the generalized Lagrange equa-tions of the second kind.Two examples are given to illustratethe theory.展开更多
In this paper by means of typical engineering examples and deep theoretical analysis, we prove that under the effect of conservative force, the Hamilton principles in holonomic and non-holonomic systems have the same...In this paper by means of typical engineering examples and deep theoretical analysis, we prove that under the effect of conservative force, the Hamilton principles in holonomic and non-holonomic systems have the same formula δ∫Ldt=0. The formula ∫δdt=0 is an evolved form of the formula δ∫Ldt=0. Therefore, the two formulas are unified.展开更多
文摘高山滑雪运动是一项技术性很强的运动,滑雪板的特性直接影响着运动的效果,因此对滑雪板的研究有很大的现实意义.用数值研究的方法,从滑雪板的几何特性出发,在转弯半径关系式的基础上推导了滑雪板转弯运动时的约束方程,建立了单刚体人体滑雪运动的广义L agrange-R ou th动力学方程,并对人体在平地和斜坡两种情况下的滑雪运动进行了数值仿真与分析.计算结果符合实际的实验结果,表明所建立的力学模型能较好地反映滑雪运动的力学特性,进而增强了对滑雪运动本质的理解,并为进一步的运动仿真提供必要的理论基础.
基金The project supported by the National Natural Science Foundation of China （10272002） and the Doctoral Program from the Ministry of Education of China （20020001032） The English text was polished by Yunming Chen.
文摘A nonlinear dynamic model of a simple nonholonomic system comprising a self-rotating cantilever beam subjected to a unilateral locked or unlocked constraint is established by employing the general Hamilton＇s Variational Principle. The critical values, at which the trivial equilibrium loses its stability or the unilateral constraint is activated or a saddle-node bifurcation occurs, and the equilibria are investigated by approximately analytical and numerical methods. The results indicate that both the buckled equilibria and the bifurcation mode of the beam are different depending on whether the distance of the clearance of unilateral constraint equals zero or not and whether the unilateral constraint is locked or not. The unidirectional snap-through phenomenon （i.e. catastrophe phenomenon） is destined to occur in the system no matter whether the constraint is lockable or not. The saddle-node bifurcation can occur only on the condition that the unilateral constraint is lockable and its clearance is nonzero. The results obtained by two methods are consistent.
文摘In this paper the Lie-form invariance of the non-holonomic systems with unilateral constraints is studied. The definition and the criterion of the Lie-form invariance of the system are given. The generalized Hojman conserved quantity and a new type of conserved quantity deduced from the Lie-form invariance are obtained. Finally, an example is presented to illustrate the application of the results.
基金The project supported by the Ministry of Science,Technologies and Development,Republic of Serbia(1874)
文摘This paper deals with the generalization of the fieldmethod to non-holonomic systems whose motion is subject toeither non-linear constraints or those of a higher order,whiletheir motion is modeled by the generalized Lagrange equa-tions of the second kind.Two examples are given to illustratethe theory.
文摘In this paper by means of typical engineering examples and deep theoretical analysis, we prove that under the effect of conservative force, the Hamilton principles in holonomic and non-holonomic systems have the same formula δ∫Ldt=0. The formula ∫δdt=0 is an evolved form of the formula δ∫Ldt=0. Therefore, the two formulas are unified.
