Hamilton’s Equations With Euler Parameters for Rigid Body Dynamics Modeling

Shivarama, Ravishankar; Fahrenthold, Eric P.

doi:10.1115/1.1649977

Cited by 36 publications

(23 citation statements)

References 12 publications

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“…The canonical Hamilton's equations for a system of rigid bodies described by the mechanical generalized coordinates of interest here are provided in Reference [33]. In this case, although the particles are rigid, the density interpolation kernel described in the kinematics and interpolation section models general non-linear compressibility effects and hence allows for accurate wave propagation simulations [21,22].…”

Section: Hamilton's Equationsmentioning

confidence: 99%

Impact dynamics simulation for multilayer fabrics

Rabb

Fahrenthold

2010

Numerical Meth Engineering

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SUMMARYHigh-strength fabrics are employed in a wide range of ballistic protection and blast mitigation applications. They are normally used in a multilayer configuration. General numerical models of impact, perforation, and fragmentation processes in multilayer fabrics must account for complex contact-impact dynamics and include general thermomechanical coupling. A hybrid particle-element formulation has been developed to simulate impact and perforation in plain weave fabrics. Simulation results show good agreement with experiment, for fragment simulating projectile impacts on both aramid and ultra high molecular weight polyethelene soft armor materials.

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Section: Hamilton's Equationsmentioning

confidence: 99%

Impact dynamics simulation for multilayer fabrics

Rabb

Fahrenthold

2010

Numerical Meth Engineering

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“…If we take the convective and inertial frame origins to be collocated, = {0 0 0}, and e = E. First, take the vector notation from Munjiza et al [11] and transform it to matrix notation as used in [1,2]. We find…”

Section: Explicit Quaternion-based Algorithmsmentioning

confidence: 99%

“…For instance, Shivarama and Fahrenthold [2] proposed a Hamiltonian formulation of the equations of motion that uses quaternions (Euler parameters) to eliminate the problem of singularities [3]. To take advantage of the attractive properties of the quaternion, Simo and Wong [3] have formulated a quaternion-based approach that utilizes an exponential map of the angle magnitude, coupled with the Newmark numerical integration method to calculate the quaternion angle at a given time step.…”

Section: Introductionmentioning

confidence: 99%

Quaternion‐based rigid body rotation integration algorithms for use in particle methods

Johnson

Williams

Cook

2007

Numerical Meth Engineering

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SUMMARYThe resolution of translational motion in discrete element method and molecular dynamics applications is a straightforward task; however, resolving rotational motion is less obvious. Many applications update rotation using an explicit integration involving products of matrices, which has well-known drawbacks. Although rigid body rotation has received attention in large-angle rotation applications, relatively little attention has been dedicated to the unique requirements of particle methods using explicit time-stepping algorithms. This paper reviews existing explicit algorithms and shows the benefits of using a quaternionbased re-parameterization of both the central difference algorithm and the approach of Munjiza et al. (Int. J. Numer. Meth. Engng 2003; 56:36-55). The improvement not only provides guaranteed orthonormality of the resulting rotation but also allows the assumption of small-angle rotation to be relaxed and the use of a more accurate Taylor expansion instead. The current and quaternion-based algorithms are compared for accuracy and computational efficiency.

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“…The definition of the kinetic energy (coming from the application of the Legendre transformation) is (see Arnold, 1978;Shivarama and Fahrenthold, 2004):…”

Section: Kinetic Energymentioning

confidence: 99%

A comprehensive dynamic model for class-1 tensegrity systems based on quaternions

Cefalo

Mirats-Tur

2011

International Journal of Solids and Structures

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In this paper we propose a new dynamic model, based on quaternions, for tensegrity systems of class-1. Quaternions are used to represent orientations of a rigid body in the 3-dimensional space eliminating the problem of singularities. Moreover, the equations based on quaternions allow to perform more precise calculations and simulations because they do not use trigonometric functions for the representation of angles. We present a thorough introduction of tensegrities and the current state of research. We also introduce the quaternions and provide in the appendix some important details and useful properties. Applying the Euler–Lagrange approach we derive a comprehensive dynamic model, first for a simple rigid bar in the space and, at last, for a class-1 tensegrity system. We present two model forms: a matrix and a vectorial form. The first more compact and easier to write, the latter more suitable to apply the tools and the theory based on vector fields.Postprint (author’s final draft

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Hamilton’s Equations With Euler Parameters for Rigid Body Dynamics Modeling

Cited by 36 publications

References 12 publications

Impact dynamics simulation for multilayer fabrics

Impact dynamics simulation for multilayer fabrics

Quaternion‐based rigid body rotation integration algorithms for use in particle methods

A comprehensive dynamic model for class-1 tensegrity systems based on quaternions

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