一种不含待定乘子的理想约束系统的动力学建模

为了克服应用罗斯方法所建立的理想约束系统的动力学方程中含有待定乘子以及方程的数目和未知变量的个数都比较多的这种缺陷,本文从广义坐标形式的动力学普遍方程出发,并结合系统的约束方程,推导出一种不含待定乘子的理想约束系统的动力学方程组,并给出了应用该方程组完成理想约束系统动力学建模的具体步骤。本文所建立的理想约束系统的动力学方程组相对于应用罗斯方法所建立的动力学方程组,具有不含待定乘子且方程和未知变量的个数都比较少的优点。文中通过两个动力学建模的实例证实了上述优点。     

任意阶非完整约束系统的Appell型方程

本文从万有D'Alembert原理出发,得到任意阶非完整约束系统的Appell型方程,在此基础上可给出本结果的推论.     

具有单面非线性非完整约束的动力学系统的运动

本文提出并研究了具有单面非线性非完整约束的动力学系统的运动问题,给出了描述系统运动的Ｂｏｌｔｚｍａｎｎ－Ｈａｍｅｌ型方程,并举例说明结果的应用。     

非完整树形多刚体系统的动力学方程

本文用Jourdain-Bertrand原理及图论的一些基本概念,导出非完整树形多刚体系统的动力学方程.当约束是完整的,且广义坐标相互独立时,则得到Wittenburg 的动力学方程,最后也由该原理得到Kane 方程. ...     

非光滑动力系统Floquet特征乘子的计算方法

对刚性约束的非线性动力系统进行研究 ,得到了该动力系统周期运动稳定性分析的Floquet特征乘子计算的半解析法。同时 ,也给出了刚性约束的线性动力系统和弹性约束 (分段光滑 )的非线性动力系统的Floquet特征乘子计算的解析法和数值方法。最后 ,针对一刚性约束的非线性动力系统 ,应用上述方法求Floquet特征乘子 ,并基于Floquet理论对周期运动的稳定性和分岔进行分析 ,将所得的结果与用Poincar啨映射方法分析的结果进行比较 ,以验证非光滑动力系统Floquet特征乘子计算方法的正确性     

论Vacco模型与Chetaev模型之间的关系

本文在深入研究非完整约束的几何性质和力学性质的基础上：（１）应用经典的Ｈａｍｉｌｔｏｎ原理推导出Ｖａｃｃｏ方程；（２）在Ｖａｃｃｏ方程的基础上，应用判定理想约束的力学原理，推导出Ｃｈｅｔａｅｖ条件，实现了从Ｖａｃｃｏ模型向Ｃｈｅｔａｅｖ模型的过渡；（３）论证了Ｖａｃｃｏ模型与Ｃｈｅｔａｅｖ模型是相辅相成的，从而统一了这两种模型。     

非线性非完整系统的碰撞方程

有关线性非完整系统的碰撞方程,已有文章[1]阐述清楚了。本文引入了δ_+-函数及δ~-函数,对非线性非完整系统进行了研究,並给出了该系统的碰撞方程。     

非完整系统正则形式的ЧАПЛЫТИН方程的一种降阶方法

文中根据能量积分进一步研究了非完整系统正则形式的ЧАПЛЫГИН方程的降阶问题,得到了处理这类系统的一般积分方法.给出的两个例子表明,该方法比文[3,4]更具优越性.     

非线性非完整系统在冲力作用时的Kane方程

Kane方程[1],[2]是建立和求解复杂系统动力学方程的有效方法。它适用于完整系统、线性非完整系统、非线性非完整系统[3]、[4]。本文从一般非线性非完整系统的Kane方程出发,建立了在冲力作用时的Kane方程,并通过算例说明该方法的优点。     

非完整系统的第一积分与其变分方程特解的联系

本文给出非完整系统的变分方程,研究它们的解,并证明在一定条件下可利用第一积分来得到变分方程的特解,最后举例说明其应用。     

Skew-gradient representations of constrained mechanical systems

The characteristics of stationary and non-stationary skew-gradient systems are studied. The skew-gradient representations of holonomic systems, Birkhoffian systems, generalized Birkhoffian systems, and generalized Hamiltonian systems are given. The characteristics of skew-gradient systems are used to study integration and stability of the solution of constrained mechanical systems. Examples are given to illustrate applications of the result.     

Model reduction for constrained mechanical systems via spectral submanifolds

Nonlinear Dynamics - Dynamical systems are often subject to algebraic constraints in conjunction with their governing ordinary differential equations. In particular, multibody systems are commonly...     

Kronecker product and a new matrix form of Lagrangian equations with multipliers for constrained multibody systems

The automatic derivation of motion equations is an important problem of multibody system dynamics. Firstly, an overview of the matrix calculus related to Kronecker product of two matrices is presented. A new matrix form of Lagrangian equations with multipliers for constrained multibody systems is then developed to demonstrate the usefulness of Kronecker product of two matrices in the study of dynamics of multibody systems. Finally, the equations of motion of mechanisms are derived using the proposed matrix form of Lagrangian equations as application examples.     

Morse families and constrained mechanical systems. Generalized hyperelastic materials

The present work deals with the geometrical desingularization of a well-known asymptotic realization of the ideal holonomic constraints in analytical mechanics. A structure of this kind is extended to the theory of continuous materials—in particular, to elastic materials with internal constraints. By using the same geometrical structure, another aim of this paper can be fulfilled: a new type of generalized hyperelastic material is introduced and some physical examples are discussed. This definition of a generalized hyperelastic material globalizes and unifies the usual definition of a hyperelastic material and its analogue for crystalline solids according to Ericksen and Pitteri. We recall that generalized hyperelastic materials can display a multi-valued strain-stress behaviour, as discussed by Ericksen. Such a behaviour can be used to describe phenomena usually regarded as typical of plasticity.

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Sommario In questo lavoro si considera una desingolarizzazione geometrica di una ben nota realizzazione asintotica dei vincoli lisci olonomi in meccanica analitica. Tale struttura è estesa allla meccanica dei continui, in particolare, al caso dei materiali elastici con vincoli interni. Utilizzando lo stesso ambiente geometrico di quest'ultima costruzione si realizza un altro scopo di questa nota: viene introdotta una nuova definizione di materiale iperelastico in senso generalizzato e sono discussi alcuni esempi fisici noti in letteratura. Questa definizione globalizza e unifica l'usuale definizione di materiale iperelastico e il suo analogo per i solidi cristallini secondo Ericksen e Pitteri. Tali materiali possono manifestare una risposta stress-strain multivoca. Questo comportamento può essere utilizzato per la descrizione di fenomenologie tipiche della plasticità.

     

Motion equations in redundant coordinates with application to inverse dynamics of constrained mechanical systems

The basis for any model-based control of dynamical systems is a numerically efficient formulation of the motion equations, preferably expressed in terms of a minimal set of independent coordinates. To this end the coordinates of a constrained system are commonly split into a set of dependent and independent ones. The drawback of such coordinate partitioning is that the splitting is not globally valid since an atlas of local charts is required to globally parameterize the configuration space. Therefore different formulations in redundant coordinates have been proposed. They usually involve the inverse of the mass matrix and are computationally rather complex. In this paper an efficient formulation of the motion equations in redundant coordinates is presented for general non-holonomic systems that is valid in any regular configuration. This gives rise to a globally valid system of redundant differential equations. It is tailored for solving the inverse dynamics problem, and an explicit inverse dynamics solution is presented for general full-actuated systems. Moreover, the proposed formulation gives rise to a non-redundant system of motion equations for non-redundantly full-actuated systems that do not exhibit input singularities.     

Connections and geodesic characteristic of equations of motion for constrained mechanical systems

I.IntroductionSinceEinsteinestablishedgeneralrelativityatthebiginningofthiscentury,differentialgeometry,especiallythemodernditTerentialgeometry,hasbeenextellsivelyappliedtomanyfieldsofphysics.Thestudyofregularholonomicmechanicalsystemsinthemodernsettingofdifferentialgeometryhasahistoryofmorethanthirtyyears.Andtheresearchtendstoperfectgraduallyt'~'l.Sinceearlyin1980'sthegeometrizationaboutconstrainedmechanicalsystemsandsingularmechanicalsystemshasbeenattachedimportanceextensivelyandsomeresult…     

Energy considerations for the stabilization of constrained mechanical systems with velocity projection

There are many difficulties involved in the numerical integration of index-3 Differential Algebraic Equations (DAEs), mainly related to stability, in the context of mechanical systems. An integrator that exactly enforces the constraint at position level may produce a discrete solution that departs from the velocity and/or acceleration constraint manifolds (invariants). This behavior affects the stability of the numerical scheme, resulting in the use of stabilization techniques based on enforcing the invariants. A coordinate projection is a post-stabilization technique where the solution obtained by a suitable DAE integrator is forced back to the invariant manifolds. This paper analyzes the energy balance of a velocity projection, providing an alternative interpretation of its effect on the stability and a practical criterion for the projection matrix selection.     

Extension of Noether's theorem to constrained non-conservative dynamical systems

A method based on a differential variational principle is developed in order to extend Noether's theorem to constrained non-conservative dynamical systems. The result is applied to generate constants of the motion for a generic example of a non-linear, dissipative dynamical system with time-varying coefficients represented by the Emden equation. The converse of Noether's theorem, whereby the symmetries of the system are determined from the knowledge of the Lagrangian and a first integral is also considered for both the Emden equation, and that of the damped harmonic oscillator. It is further shown that the presence of ideal constraints (whether holonomic or non-holonomic) does not affect the statement of Noether's theorem. The constraints affect the Jacobi energy integral, however, because they enter into consideration through real work instead of virtual work. It is shown that the Jacobi integral is conserved provided that: (a) the Lagrangian is explicitly independent of time, (b) the real power of the generalized forces not derivable from a potential vanish, (c) the holonomic constraints are explicitly independent of time, (d) the non-holonomic constraints are linear and homogeneous in the generalized velocities.