Formulas for Dynamic Analysis

Huston, Ronald L.; Liu, CQ; Ángeles, Jorge

doi:10.1115/1.1445305

Cited by 4 publications

(7 citation statements)

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“…1 A generalized force polygon representing Equation (21) Equation (23) may be called "Kane's equations with nonideal constraint forces." For ideally constrained systems (with C = 0), Equation (23) reduces to the standard form of Kane's equations [13].…”

Section: Interpretation Via Kane's Equationsmentioning

confidence: 99%

“…Then, an elementary dynamic analysis shows that the equations of motion of the unconstrained system may be expressed as [21]: where…”

Section: Examplementioning

confidence: 99%

“…In this unconstrained state, the equations of motion may be written as (Huston [17], Huston and Liu [21]):…”

Section: Preliminary Considerations and Equation Developmentmentioning

confidence: 99%

“…, n), and f is an n × 1 column array of generalized applied forces and generalized inertia force terms (including the so-called "centrifugal" and "Coriolis" terms). Let S be subjected to m(m < n) holonomic and/or "simple" nonholonomic constraints [17,21]. S will then be reduced to having n − m degrees of freedom.…”

Section: Preliminary Considerations and Equation Developmentmentioning

confidence: 99%

“…The determination of W, as well as V, in Equation (12) may be accomplished in several ways including the use of the zero eigenvalues theorem as developed by Walton and Steeves et al [17,21,26,27]. See also Singh and Likins [14].…”

Section: Interpretation Via Kane's Equationsmentioning

confidence: 99%

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Another form of equations of motion for constrained multibody systems

Liu

Huston

2007

Nonlinear Dyn

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This paper presents a new and simplified set of explicit equations of motion for constrained mechanical systems. The equations are applicable with both holonomic and nonholonomic systems and the constraints may, or may not, be ideal. It is shown that this set of equations is equivalent to governing equations developed earlier by others. The connection of these equations with Kane's equations is discussed. It is shown that the developed equations are directly applicable with controlled systems where the controlling forces and moments may be subject to constraints. Finally, a procedure is presented for determining which control force systems are equivalent. Examples are presented to demonstrate the advantages, features, and range of application of the equations.

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Section: Interpretation Via Kane's Equationsmentioning

confidence: 99%

“…Then, an elementary dynamic analysis shows that the equations of motion of the unconstrained system may be expressed as [21]: where…”

Section: Examplementioning

confidence: 99%

“…In this unconstrained state, the equations of motion may be written as (Huston [17], Huston and Liu [21]):…”

Section: Preliminary Considerations and Equation Developmentmentioning

confidence: 99%

Section: Preliminary Considerations and Equation Developmentmentioning

confidence: 99%

Section: Interpretation Via Kane's Equationsmentioning

confidence: 99%

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Another form of equations of motion for constrained multibody systems

Liu

Huston

2007

Nonlinear Dyn

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A SPH framework for dynamic interaction between soil and rigid body system with hybrid contact method

Zhan

Peng

Zhang

et al. 2020

Num Anal Meth Geomechanics

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A smoothed particle hydrodynamics (SPH) framework for three-dimensional dynamic soil-multibody interaction modeling is presented, where both soils and rigid bodies are discretized using SPH particles. In the framework, soils are modeled using the Drucker-Prager model, while rigid bodies are considered with a multibody dynamics solver. A hybrid contact method suitable for three-dimensional simulations is developed to model the soil-body and body-body frictionless and frictional contacts, where contact forces are calculated based on ideal plastic collision and the unit normal/tangential vectors of the actual surface. Owing to its simplicity in contact detection and accuracy in contact force calculation, the hybrid contact method can be easily incorporated into SPH. Furthermore, graphics processing unit (GPU) parallelization is utilized to improve efficiency. The presented numerical framework and the hybrid contact method are validated using several examples. Numerical results are compared with analytical solutions and results from the literature. Furthermore, two three-dimensional simulations involving dynamic soil-multibody interaction are included to demonstrate the application.

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A momentum form of Kane’s equations for scleronomic systems

Phillips

Amirouche

2017

Mathematical and Computer Modelling of Dynamical Systems

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Kane's dynamical equations are an efficient and widely used method for deriving the equations of motion for multibody systems. Despite their popularity, no publication has appeared which adapts them for use with port-based modelling tools such as bond graphs, linear graphs or port-Hamiltonian theory. In this paper, we presentfor scleronomic systems a momentum form of Kane's equations, fully compatible with portbased modelling methods. When applied to holonomic systems using coordinate derivatives, the momentum form of Kane's equations is an efficient alternative to Lagrange's equations, providing a momentum formulation without the need to assemble and differentiate the system kinetic co-energy function. When applied to holonomic or nonholonomic systems using generalized speeds, a rotational decomposition of the generalized forces leads to a convenient set of matrix equations of motion, for which a system-level multibond graph interpretation is given. Heuristics are provided for selection of generalized speeds which, for systems with open-chain kinematics, produce a block-diagonal mass matrix and reduce the complexity of the equations from order-N 3 to order-N. For scleronomic systems, the momentum formulation retains all analysis capabilities offered by the original acceleration formulation. Two example problems are solved with the momentum formulation, including the nonholonomic rolling thin disk.

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Formulas for Dynamic Analysis

Cited by 4 publications

References 0 publications

Another form of equations of motion for constrained multibody systems

Another form of equations of motion for constrained multibody systems

A SPH framework for dynamic interaction between soil and rigid body system with hybrid contact method

A momentum form of Kane’s equations for scleronomic systems

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