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Research Papers

Extension of Maggi and Kane Equations to Holonomic Dynamic Systems

[+] Author and Article Information
Edward J. Haug

Carver Distinguished Professor Emeritus
Department of Mechanical Engineering,
The University of Iowa,
Iowa City, IA 52242
e-mail: echaug@gmail.com

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received June 18, 2018; final manuscript received September 16, 2018; published online October 15, 2018. Assoc. Editor: Paramsothy Jayakumar.

J. Comput. Nonlinear Dynam 13(12), 121003 (Oct 15, 2018) (6 pages) Paper No: CND-18-1275; doi: 10.1115/1.4041579 History: Received June 18, 2018; Revised September 16, 2018

The Maggi and Kane equations of motion are valid for systems with only nonholonomic constraints, but may fail when applied to systems with holonomic constraints. A tangent space ordinary differential equation (ODE) extension of the Maggi and Kane formulations that enforces holonomic constraints is presented and shown to be theoretically sound and computationally effective. Numerical examples are presented that demonstrate the extended formulation leads to solutions that satisfy position, velocity, and acceleration constraints for holonomic systems to near computer precision.

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References

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Figures

Grahic Jump Location
Fig. 1

Projection onto constraint manifold

Grahic Jump Location
Fig. 2

Continuation of solution trajectory over charts

Grahic Jump Location
Fig. 3

Heavy symmetric top with tip constrained to xy plane

Grahic Jump Location
Fig. 4

Two body spatial pendulum

Tables

Errata

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