Rigid Body Impact Modeling Using Integral Formulation

Zhang, Yuning; Sharf, Inna

doi:10.1115/1.2389232

Cited by 5 publications

(2 citation statements)

References 8 publications

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“…Although only the ending point of the hodograph is needed to determine the tangential impulse accumulation during the slip, generally there is no short cut to locate this point other than numerical integration. Stable (but not efficient) numerical integration methods were investigated by Zhao and Liu (2007), and Zhang and Sharf (2007). Slow integration hinders not just the modeling effort but also, in a broader sense, application of impact to real tasks where modeling may be executed as a subroutine many times by some higher level modeling or planning algorithm.…”

Section: Introductionmentioning

confidence: 99%

Analysis and Computation of Two Body Impact in Three Dimensions

Jia

Wang

2017

Journal of Computational and Nonlinear Dynamics

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A formal impulse-based analysis is presented for the collision of two rigid bodies at single contact point under Coulomb's friction in three dimensions (3D). The tangential impulse at the contact is known to be linear in the sliding velocity whose trajectory, parametrized with the normal impulse and referred to as the hodograph, is governed by a generally nonintegrable ordinary differential equation (ODE). Evolution of the hodograph is bounded by rays in several invariant directions of sliding in the contact plane. Exact lower and upper bounds are derived for the number of such invariant directions, utilizing the established positive definiteness of the matrix defining the governing ODE. If the hodograph reaches the origin, it either terminates (i.e., the contact sticks) or continues in a new direction (i.e., the contact resumes sliding) whose existence and uniqueness, only assumed in the literature, are proven. Closed-form integration of the ODE becomes possible as soon as the sliding velocity turns zero or takes on an invariant direction. Assuming Stronge's energy-based restitution, a complete algorithm is described to combine fast numerical integration (NI) with a case-by-case closed-form analysis. A number of solved collision instances are presented. It remains open whether the modeled impact process will always terminate under Coulomb's friction and Stronge's (or Poisson's) restitution hypothesis.

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Section: Introductionmentioning

confidence: 99%

Analysis and Computation of Two Body Impact in Three Dimensions

Jia

Wang

2017

Journal of Computational and Nonlinear Dynamics

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“…In recent years, many researchers rediscover the Routh model [2], analyzing it in detail [4] and also applying it in modeling of relatively simple problems concerning collisions of free bodies [5] as well as collisions in the multi-body systems with impacts [6]. On the base of Routh's model, some more advanced models have been recently developed [3,7,8].…”

Section: Introductionmentioning

confidence: 99%

Motion of double pendulum colliding with an obstacle of rough surface

2017

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The externally excited and damped vibration of the double pendulum in the vertical plane are considered. The pendulum can collide many times during the motion with a motionless obstacle having the rough surface. The double pendulum colliding with this object has been modeled as a piecewise smooth system constrained by the unilateral constraint. In the relatively long time between the collisions, the differential equations govern the motion of the pendulum. When the contact with the obstacle appears, the pendulum exhibits a discontinuous behavior. An important element of the solving algorithm is aimed on the continuous tracking of the position of the pendulum in order to detect the collision with the unilateral constraints and to determine the state vector of the pendulum at the impact time instant. A single collision is described by the Euler's laws of motion in the integral form. The equations are supplemented by the Poisson's hypothesis and Coulomb's law of friction. The friction law is formulated for the instantaneous values of the reaction forces. The values of their impulses depend on the existence of a slip between the contacting bodies. Therefore, the Coulomb law cannot be generalized for the linear impulses of the forces in a simple way. We have applied the Routh method in order to solve the problem. The method has a simple geometrical interpretation in the impulse space. The angular velocities of both pendulum parts as well as the reaction forces at the joints of the system, which change in stepwise manner, have been presented in the paper.

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Contact mechanics for dynamical systems: a comprehensive review

Flores

2021

Multibody Syst Dyn

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Rigid Body Impact Modeling Using Integral Formulation

Cited by 5 publications

References 8 publications

Analysis and Computation of Two Body Impact in Three Dimensions

Analysis and Computation of Two Body Impact in Three Dimensions

Motion of double pendulum colliding with an obstacle of rough surface

Contact mechanics for dynamical systems: a comprehensive review

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