484 Discrete Holonomic Hamiltonian system with Geometric Constraint Stabilization

2009 ◽  
Vol 2009 (0) ◽  
pp. _484-1_-_484-5_
Author(s):  
Kenji SOYA ◽  
Hiroaki YOSHIMURA
Keyword(s):  
Hamiltonian System ◽  
Geometric Constraint ◽  
Constraint Stabilization

On the Geometric Stabilization for Discrete Hamiltonian Systems With Holonomic Constraints

2009 ◽  
Author(s):  
Hiroaki Yoshimura ◽  
Kenji Soya
Keyword(s):  
Hamiltonian System ◽  
Hamiltonian Systems ◽  
Geometric Constraint ◽  
Differentiation Formula ◽  
Holonomic Constraints ◽  
Constrained Mechanical Systems ◽  
Constraint Stabilization ◽  
Backward Differentiation Formula ◽  
External Forces ◽  
Baumgarte Stabilization

This paper develops a discrete Hamiltonian system with holonomic constraints with Geometric Constraint Stabilization. It is first shown that constrained mechanical systems with nonconservative external forces can be formulated by using canonical symplectic structures in the context of Hamiltonian systems. Second, it is shown that discrete holonomic Hamiltonian systems can be developed via the discretization based on the Backward Differentiation Formula and also that geometric constraint stabilization can be incorporated into the discrete Hamiltonian systems. It is demonstrated that the proposed method enables one to stabilize constraint violations effectively in comparison with conventional methods such as Baumgarte Stabilization and Gear–Gupta–Leimkuhler Stabilization, together with an illustrative example of linkage mechanisms.

Discrete Constrained Lagrangian Systems and Geometric Constraint Stabilization

2010 ◽  
Author(s):  
Hiroaki Yoshimura ◽  
Azumi Yoshida ◽  
Theodore E. Simos ◽  
George Psihoyios ◽  
Ch. Tsitouras
Keyword(s):  
Geometric Constraint ◽  
Lagrangian Systems ◽  
Constraint Stabilization

A Geometric Approach to Constraint Stabilization for Holonomic Lagrangian Systems

2007 ◽  
Author(s):  
Hiroaki Yoshimura
Keyword(s):  
Mechanical Systems ◽  
Geometric Approach ◽  
Geometric Constraint ◽  
Lagrangian System ◽  
Lagrangian Systems ◽  
Numerical Verification ◽  
Linkage Mechanism ◽  
Constraint Stabilization ◽  
D’Alembert Principle ◽  
Configuration Manifold

In this paper, we develop a geometric approach to constraint stabilization for holonomic mechanical systems in the context of Lagrangian formulation. We first show that holonomic mechanical systems, for the case in which a given Lagrangian is hyperregular, can be formulated by using the Lagrangian two-form, namely, a symplectic structure on the tangent bundle of a configuration manifold that is induced from the cotangent bundle via the Legendre transformation. Then, we present an idea of geometric constraint stabilization and we show that a holonomic Lagrangian system with geometric constraint stabilization can be formulated by the Lagrange-d’Alembert principle, together with its local coordinate expression for the sake of numerical computations. Finally, we illustrate the numerical verification that the proposed method enables to stabilize constraint violations effectively in comparison with the Baumgarte and Gear–Gupta–Leimkuhler methods together with an example of a linkage mechanism.

scholarly journals Hamiltonian Approach to Magnetic Fields with Toroidal Surfaces

1985 ◽  
Vol 40 (10) ◽  
pp. 959-967
Author(s):  
A. Salat
Keyword(s):  
Magnetic Field ◽  
Hamiltonian System ◽  
Magnetic Fields ◽  
Constant Pressure ◽  
Time Dependent ◽  
Hamiltonian Approach ◽  
One Dimensional ◽  
Mhd Equilibrium ◽  
Magnetic Surfaces ◽  
Rotational Transform

The equivalence of magnetic field line equations to a one-dimensional time-dependent Hamiltonian system is used to construct magnetic fields with arbitrary toroidal magnetic surfaces I = const. For this purpose Hamiltonians H which together with their invariants satisfy periodicity constraints have to be known. The choice of H fixes the rotational transform η(I). Arbitrary axisymmetric fields, and nonaxisymmetric fields with constant η(I) are considered in detail.Configurations with coinciding magnetic and current density surfaces are obtained. The approach used is not well suited, however, to satisfying the additional MHD equilibrium condition of constant pressure on magnetic surfaces.

Dynamic Buckling of Cylindrical Shells under Axial Impact in Hamiltonian System

2012 ◽  
Vol 13 (1) ◽  
Author(s):  
Jia-Bin Sun ◽  
Xin-Sheng Xu ◽  
Chee-Wah Lim
Keyword(s):  
Hamiltonian System ◽  
Critical Load ◽  
Impact Load ◽  
Dynamic Buckling ◽  
Inertia Force ◽  
Elastic Cylindrical Shell ◽  
Symplectic Method ◽  
Buckling Mode ◽  
Axial Impact ◽  
Dual Variables

AbstractIn this paper, the dynamic buckling of an elastic cylindrical shell subjected to an axial impact load is analyzed in Hamiltonian system. By employing a symplectic method, the traditional governing equations are transformed into Hamiltonian canonical equations in dual variables. In this system, the critical load and buckling mode are reduced to solving symplectic eigenvalues and eigensolutions respectively. The result shows that the critical load relates with boundary conditions, thickness of the shell and radial inertia force. And the corresponding buckling modes present some local shapes. Besides, the process of dynamic buckling is related to the stress wave, the critical load and buckling mode depend upon the impacted time. This paper gives analytically and numerically some new rules of the buckling problem, which is useful for designing shell structures.

scholarly journals Constraint and Mobility Change Analysis of Rubik’s Cube-inspired Reconfigurable Joints and Corresponding Parallel Mechanisms

2020 ◽  
Vol 33 (1) ◽  
Author(s):  
Duanling Li ◽  
Pu Jia ◽  
Jiazhou Li ◽  
Dan Zhang ◽  
Xianwen Kong
Keyword(s):  
Parallel Mechanism ◽  
Unique Feature ◽  
Theoretical Method ◽  
Geometric Constraint ◽  
Parallel Mechanisms ◽  
Change Analysis ◽  
Application Range ◽  
And Topology ◽  
Physical Experiments ◽  
Underlying Principle

Abstract The current research of reconfigurable parallel mechanism mainly focuses on the construction of reconfigurable joints. Compared with the method of changing the mobility by physical locking joints, the geometric constraint has good controllability, and the constructed parallel mechanism has more configurations and wider application range. This paper presents a reconfigurable axis (rA) joint inspired and evolved from Rubik's Cubes, which have a unique feature of geometric and physical constraint of axes of joint. The effectiveness of the rA joint in the construction of the limb is analyzed, resulting in a change in mobility and topology of the parallel mechanism. The rA joint makes the angle among the three axes inside the groove changed arbitrarily. This change in mobility is completed by the case illustrated by a 3(rA)P(rA) reconfigurable parallel mechanism having variable mobility from 1 to 6 and having various special configurations including pure translations, pure rotations. The underlying principle of the metamorphosis of this rA joint is shown by investigating the dependence of the corresponding screw system comprising of line vectors, leading to evolution of the rA joint from two types of spherical joints to three types of variable Hooke joints and one revolute joint. The reconfigurable parallel mechanism alters its topology by rotating or locking the axis of rA joint to turn all limbs into different phases. The prototype of reconfigurable parallel mechanism is manufactured and all configurations are enumerated to verify the validity of the theoretical method by physical experiments.

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