Efficient formulation of the Gibbs–Appell equations for constrained multibody systems

2021 ◽  
Author(s):  
S. M. Mirtaheri ◽  
Hassan Zohoor
Keyword(s):  
Multibody Systems ◽  
Constrained Multibody Systems ◽  
Appell Equations

On the Use of the Canonical Equations of Motion for the Dynamic Analysis of Constrained Multibody Systems

1992 ◽  
Author(s):  
E. Bayo ◽  
J. M. Jimenez
Keyword(s):  
Dynamic Analysis ◽  
Multibody Systems ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Numerical Algorithms ◽  
Constrained Multibody Systems ◽  
Constrained Mechanical Systems ◽  
First Order ◽  
Canonical Variables ◽  
Lagrange’S Multipliers

Abstract We investigate in this paper the different approaches that can be derived from the use of the Hamiltonian or canonical equations of motion for constrained mechanical systems with the intention of responding to the question of whether the use of these equations leads to more efficient and stable numerical algorithms than those coming from acceleration based formalisms. In this process, we propose a new penalty based canonical description of the equations of motion of constrained mechanical systems. This technique leads to a reduced set of first order ordinary differential equations in terms of the canonical variables with no Lagrange’s multipliers involved in the equations. This method shows a clear advantage over the previously proposed acceleration based formulation, in terms of numerical efficiency. In addition, we examine the use of the canonical equations based on independent coordinates, and conclude that in this second case the use of the acceleration based formulation is more advantageous than the canonical counterpart.

Dynamics of Flexible Beams and Plates in Large Overall Motions

1992 ◽  
Vol 59 (4) ◽  
pp. 991-999 ◽  
Author(s):  
Z. E. Boutaghou ◽  
Arthur G. Erdman ◽  
Henryk K. Stolarski
Keyword(s):  
Dynamic Response ◽  
Nonlinear Interaction ◽  
Multibody Systems ◽  
Present Theory ◽  
Rigid Body Dynamics ◽  
Flexible Beams ◽  
Constrained Multibody Systems ◽  
Dynamic Stiffening ◽  
Body Dynamics ◽  
Arbitrary Representation

The dynamic response of flexible beams, plates, and solids undergoing arbitrary spatial motions are systematically derived via a proposed approach. This formulation is capable of incorporating arbitrary representation of the kinematics of deformation, phenomenon of dynamic stiffening, and complete nonlinear interaction between elastic and rigid-body dynamics encountered in constrained multibody systems. It is shown that the present theory captures the phenomenon of dynamic stiffening due to the transfer of the axial and membrane forces to the bending equations of beams and plates, respectively. Examples are presented to illustrate the proposed formulations.

scholarly journals Constraint Gradient Projective Method for Stabilized Dynamic Simulation of Constrained Multibody Systems

2003 ◽  
Author(s):  
Zdravko Terze ◽  
Joris Naudet ◽  
Dirk Lefeber
Keyword(s):  
Mathematical Models ◽  
Dynamic Simulation ◽  
Multibody Systems ◽  
Point Of View ◽  
Constraint Violation ◽  
Projective Method ◽  
Holonomic Constraints ◽  
Constrained Multibody Systems ◽  
Constrained Mechanical Systems ◽  
Holonomic Systems

Constraint gradient projective method for stabilization of constraint violation during integration of constrained multibody systems is in the focus of the paper. Different mathematical models for constrained MBS dynamic simulation on manifolds are surveyed and violation of kinematical constraints is discussed. As an extension of the previous work focused on the integration procedures of the holonomic systems, the constraint gradient projective method for generally constrained mechanical systems is discussed. By adopting differentialgeometric point of view, the geometric and stabilization issues of the method are addressed. It is shown that the method can be applied for stabilization of holonomic and non-holonomic constraints in Pfaffian and general form.

scholarly journals Online Kinematic and Dynamic-State Estimation for Constrained Multibody Systems Based on IMUs

Sensors ◽  
2016 ◽  
Vol 16 (3) ◽  
pp. 333 ◽  
Author(s):  
José Torres-Moreno ◽  
José Blanco-Claraco ◽  
Antonio Giménez-Fernández ◽  
Emilio Sanjurjo ◽  
Miguel Naya
Keyword(s):  
State Estimation ◽  
Multibody Systems ◽  
Dynamic State ◽  
Constrained Multibody Systems ◽  
Dynamic State Estimation

Dynamics of Constrained Multibody Systems

1984 ◽  
Vol 51 (4) ◽  
pp. 899-903 ◽  
Author(s):  
J. W. Kamman ◽  
R. L. Huston
Keyword(s):  
Multibody Systems ◽  
Equations Of Motion ◽  
Governing Equations ◽  
Dynamical Equations ◽  
Closed Loops ◽  
Constrained Multibody Systems ◽  
Constraint Equations ◽  
Cable Dynamics ◽  
Hanging Chain ◽  
A Chain

A new automated procedure for obtaining and solving the governing equations of motion of constrained multibody systems is presented. The procedure is applicable when the constraints are either (a) geometrical (for example, “closed-loops”) or (b) kinematical (for example, specified motion). The procedure is based on a “zero eigenvalues theorem,” which provides an “orthogonal complement” array which in turn is used to contract the dynamical equations. This contraction, together with the constraint equations, forms a consistent set of governing equations. An advantage of this formulation is that constraining forces are automatically eliminated from the analysis. The method is applied with Kane’s equations—an especially convenient set of dynamical equations for multibody systems. Examples of a constrained hanging chain and a chain whose end has a prescribed motion are presented. Applications in robotics, cable dynamics, and biomechanics are suggested.

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