Mathematical Model of Interaction of a Symmetric Top with an Axially Symmetric External Field

A symmetric top is considered, which is a particular case of a mechanical top that is usually described by the canonical Poisson structure on T^*SE (3). This structure is invariant under the right action of the rotation group SO(3), but the Hamiltonian of the symmetric top is invariant only under the right action of the subgroup S ¹, which corresponds to the rotation of the symmetric top around its axis of symmetry. This Poisson structure is obtained as the reduction T^* SE (3) / S ¹. A Hamiltonian and motion equations are proposed that describe a wide class of interaction models of the symmetric top with an axially symmetric external field.     

Forward Dynamics of Open-Loop Multibody Mechanisms Using an Efficient Recursive Algorithm Based on Canonical Momenta

A new method for establishing the equations of motion of multibodymechanisms based on canonical momenta is introduced in this paper.In absence of constraints, the proposed forward dynamicsformulation results in a Hamiltonian set of 2n first order ODEsin the generalized coordinates q and the canonical momenta p.These Hamiltonian equations are derived from a recursiveNewton–Euler formulation. As an example, it is shown how, in thecase of a serial structure with rotational joints, an O(n)formulation is obtained. The amount of arithmetical operations isconsiderably less than acceleration based O(n) formulations.     

Composite rigid body formalism for flexible multibody systems

The paper describes the extension of the composite rigid body formalism for the flexible multibody systems. The extension has been done in such a way that all advantages of the formalism with respect to the coordinates of large motion of rigid bodies are extended to the flexible degrees of freedom, e.g. the same recursive treatment of both coordinates and no appearance of O(n ³) computational complexity terms due to the flexibility. This extension has been derived for both open loop and closed loop systems of flexible bodies. The comparison of the computational complexity of this formalism with other known approaches has shown that the described formalism of composite rigid body and the residual algorithm based on it are more efficient formalisms for small number of bodies in the chains and deformation modes than the usual recursive formalism of articulated body inertia.     

Solving Third Order Differential Equations with Maximal Symmetry Group

The largest group of Lie symmetries that a third-order ordinary differential equation (ode) may allow has seven parameters. Equations sharing this property belong to a single equivalence class with a canonical representative v ^′′′(u)=0. Due to this simple canonical form, any equation belonging to this equivalence class may be identified in terms of certain constraints for its coefficients. Furthermore a set of equations for the transformation functions to canonical form may be set up for which large classes of solutions may be determined algorithmically. Based on these steps a solution algorithm is described for any equation with this symmetry type which resembles a similar scheme for second order equations with projective symmetry group. Received March 9, 2000; revised June 8, 2000     

Linear closed-loop control in linear periodic systems with application to spin-stabilized bodies

A method is presented which solves the problem of determining the T-periodic feedback matrix K(t) of a linear periodic system (A(t), B(t) and C(t)), such that the closed-loop system has a desired stability property. The results are used to solve the problem of aligning the angular momentum and the spin axis of a spin-stabilized body with an inertial reference direction.     

模拟集成电路二维Stack生成及模块合并算法

在模拟集成电路设计中,关于X轴和y轴同时对称的Stack,以及模块之间的合并,对于增加器件之间的匹配和控制寄生是至关重要的.描述了模拟集成电路二轴对称Stack生成算法和模块合并算法.通过对于对称欧拉图和对称欧拉路径的研究,得出了多项理论结果.在此基础上,提出了时间复杂度为O(n)的伪器件插入算法、对称欧拉路径构造算法和二轴对称Stack生成算法.生成的Stack,不但关于X轴和y轴对称,而且具有公共质心(commoncentroid)的结构.还描述了模块合并算法,给出了计算最大合并距离的公式.该算法本质上是独立于任何拓扑表示的.实验结果验证了算法的有效性.     

New results on the relationship between dynamic programming and the maximum principle

The dynamic programming approach to optimal control theory attempts to characterize the value functionV as a solution to the Hamilton-Jacobian-Bellman equation. Heuristic arguments have long been advanced relating the Pontryagin maximum principle and dynamic programming according to the equation (H(t, x ^* (t), u ^* (t), p(t)),−p(t))=√V(t,x ^* (t)), where (x^*, u^*) is the optimal control process under consideration,p(t), is the coextremal, andH is the Hamiltonian. The relationship has previously been verified under only very restrictive hypotheses. We prove new results, establishing the relationship, now expressed in terms of the generalized gradient ofV, for a large class of nonsmooth problems.