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

A combination of Euler parameter kinematics and Hamiltonian mechanics provides a rigid body dynamics model well suited for use in strongly nonlinear problems involving arbitrarily large rotations. The model is unconstrained, free of singularities, includes a general potential energy function and a minimum set of momentum variables, and takes an explicit state space form convenient for numerical implementation. The general formulation may be specialized to address particular applications, as illustrated in several three dimensional example problems.

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Investigation of a method for the three-dimensional rigid body dynamics inverse problem

Multibody System Dynamics ◽

10.1007/s11044-011-9290-7 ◽

2012 ◽

Vol 27 (4) ◽

pp. 423-435 ◽

Cited By ~ 2

Author(s):

David M. Trujillo ◽

Henry R. Busby

Keyword(s):

Inverse Problem ◽

Rigid Body ◽

Three Dimensional ◽

Rigid Body Dynamics ◽

Body Dynamics

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Technical issues on simulating impulse and friction in three dimensional rigid body dynamics

Proceedings Computer Animation '98 (Cat. No.98EX169) ◽

10.1109/ca.1998.681922 ◽

2002 ◽

Cited By ~ 1

Author(s):

K. Kawachi ◽

H. Suzuki ◽

F. Kimura

Keyword(s):

Rigid Body ◽

Three Dimensional ◽

Rigid Body Dynamics ◽

Body Dynamics ◽

Technical Issues

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Validation of a Computational Musculoskeletal Model of the Elbow

ASME 2007 Summer Bioengineering Conference ◽

10.1115/sbc2007-176509 ◽

2007 ◽

Cited By ~ 1

Author(s):

Justin P. Fisk ◽

Jennifer S. Wayne

Keyword(s):

Rigid Body ◽

Degrees Of Freedom ◽

Three Dimensional ◽

Rigid Body Dynamics ◽

Clinical Tool ◽

Element Analysis ◽

Reconstructive Procedures ◽

Biomechanical Models ◽

Musculoskeletal Models ◽

Body Dynamics

Musculoskeletal computational modeling can be a powerful and useful tool to study joint behavior, examine muscle and ligament function, measure joint contact pressures, simulate injury, and analyze the biomechanical results of reconstructive procedures. Commonly, biomechanical models are based on either finite element analysis (FEA) or three-dimensional rigid body dynamics. While each approach has advantages for specific applications, rigid body dynamics algorithms are highly efficient [1], thus significantly reducing solution time. Many musculoskeletal models of the elbow have been developed [2, 3], but all have constrained the articulations to have particular degrees of freedom and ignored the effects of ligaments. An accurate and robust model without these limitations has potential as a clinical tool to predict the outcome of injuries and/or surgical procedures. This work develops and validates an accurate computational model of the elbow joint whereby joint kinematics are dictated by three-dimensional bony geometry contact, ligamentous constraints, and muscle loading.

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Coupled CFD and Rigid Body Dynamics Modeling of a Spinning Body with Flow Control

2nd AIAA Flow Control Conference ◽

10.2514/6.2004-2317 ◽

2004 ◽

Cited By ~ 1

Author(s):

Jubaraj Sahu

Keyword(s):

Rigid Body ◽

Flow Control ◽

Rigid Body Dynamics ◽

Dynamics Modeling ◽

Body Dynamics

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An Investigation on the Issues in Modelling of Free Flight in Animal Locomotion

ASME-JSME-KSME 2011 Joint Fluids Engineering Conference: Volume 1, Symposia – Parts A, B, C, and D ◽

10.1115/ajk2011-19018 ◽

2011 ◽

Author(s):

Masateru Maeda ◽

Toshiyuki Nakata ◽

Hao Liu

Keyword(s):

Rigid Body ◽

Degrees Of Freedom ◽

Aerodynamic Force ◽

Three Dimensional ◽

Micro Air Vehicles ◽

Rigid Body Dynamics ◽

Free Flight ◽

Comprehensive Investigation ◽

Body Dynamics ◽

Generation Mechanisms

Aiming at establishing an effective computational framework to accurately predict free-flying dynamics and aerodynamics we here present a comprehensive investigation on some issues associated with the modelling of free flight. Free flight modelling/simulation is essential for some types of flights e.g. falling leaves or auto-rotating seeds for plants; unsteady manoeuvres such as take-off, turning, or landing for animals. In addition to acquiring the deeper understanding of the flight biomechanics of those natural organisms, revealing the sophisticated aerodynamic force generation mechanisms employed by them may be useful in designing man-made flying-machines such as rotary or flapping micro air vehicles (MAVs). The simulations have been conducted using the coupling of computational fluid dynamics (CFD) and rigid body dynamics, thus achieving the free flight. The flow field is computed with a three-dimensional unsteady incompressible Navier-Stokes solver using pseudo-compressibility and overset gird technique. The aerodynamic forces acting on the flyer are calculated by integrating the forces on the surfaces. Similarly, the aerodynamic torque around the flyer’s centre of mass is obtained. The forces and moments are then introduced into a six degrees-of-freedom rigid body dynamics solver which utilises unit quaternions for attitude description in order to avoid singular attitude. Results are presented of a single body model and some insect-like multi-body models with flapping wings, which point to the importance of free-flight modelling in systematic analyses of flying aerodynamics and manoeuvrability. Furthermore, a comprehensive investigation indicates that the framework is capable to predict the aerodynamic performance of free-flying or even free-swimming animals in an intermediate range of Reynolds numbers (< 105).

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Addenda to “On Singularity of Rigid-Body Dynamics Using Quaternion-Based Models”

Journal of Applied Mechanics ◽

10.1115/1.4023108 ◽

2013 ◽

Vol 80 (4) ◽

Author(s):

Homin Choi ◽

Bingen Yang

Keyword(s):

Rigid Body ◽

Inertial Frame ◽

Three Dimensional ◽

Rigid Bodies ◽

Rigid Body Dynamics ◽

Coordinate Systems ◽

Body Frame ◽

Modeling And Analysis ◽

Body Dynamics

Although quaternions are singularity-free in modeling and analysis of rigid bodies in three-dimensional motion, description of torques may lead to unbounded response of a quaternion-based model. This paper gives theorems on the conditions of torque-induced singularity in four coordinate systems: inertial frame, body frame, Euler basis, and dual Euler basis. According to the theorems, torques applied in an inertial frame or a body frame or a Euler basis will never cause unbounded motion; torques applied in a dual Euler basis, however, may lead to unbounded motion.

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