1,445 research outputs found
Relaxation of Wobbling Asteroids and Comets. Theoretical Problems. Perspectives of Experimental Observation
A body dissipates energy when it freely rotates about any axis different from
principal. This entails relaxation, i.e., decrease of the rotational energy,
with the angular momentum preserved. The spin about the major-inertia axis
corresponds to the minimal kinetic energy, for a fixed angular momentum. Thence
one may expect comets and asteroids (as well as spacecraft or cosmic-dust
granules) stay in this, so-called principal, state of rotation, unless they are
forced out of this state by a collision, or a tidal interaction, or cometary
jetting, or by whatever other reason. As is well known, comet P/Halley,
asteroid 4179 Toutatis, and some other small bodies exhibit very complex
rotational motions attributed to these objects being in non-principal states of
spin. Most probably, the asteroid and cometary wobble is quite a generic
phenomenon. The theory of wobble with internal dissipation has not been fully
developed as yet. In this article we demonstrate that in some spin states the
effectiveness of the inelastic-dissipation process is several orders of
magnitude higher than believed previously, and can be measured, by the
presently available observational instruments, within approximately a year
span. We also show that in some other spin states both the precession and
precession-relaxation processes slow down considerably. (We call it
near-separatrix lingering effect.) Such spin states may evolve so slowly that
they can mimic the principal-rotation state.Comment: 2 figure
Chain Paradoxes
For nearly two centuries the dynamics of chains have offered examples of
paradoxical theoretical predictions. Here we propose a theory for the
dissipative dynamics of one-dimensional continua with singularities which
provides a unified treatment for chain problems that have suffered from
paradoxical solutions. These problems are duly solved within the present theory
and their paradoxes removed---we hope
Impact-induced acceleration by obstacles
We explore a surprising phenomenon in which an obstruction accelerates,
rather than decelerates, a moving flexible object. It has been claimed that the
right kind of discrete chain falling onto a table falls \emph{faster} than a
free-falling body. We confirm and quantify this effect, reveal its complicated
dependence on angle of incidence, and identify multiple operative mechanisms.
Prior theories for direct impact onto flat surfaces, which involve a single
constitutive parameter, match our data well if we account for a characteristic
delay length that must impinge before the onset of excess acceleration. Our
measurements provide a robust determination of this parameter. This supports
the possibility of modeling such discrete structures as continuous bodies with
a complicated constitutive law of impact that includes angle of incidence as an
input.Comment: small changes and corrections, added reference
Nonsmooth Lagrangian mechanics and variational collision integrators
Variational techniques are used to analyze the problem of rigid-body dynamics with impacts. The theory of smooth Lagrangian mechanics is extended to a nonsmooth context appropriate for collisions, and it is shown in what sense the system is symplectic and satisfies a Noether-style momentum conservation theorem.
Discretizations of this nonsmooth mechanics are developed by using the methodology of variational discrete mechanics. This leads to variational integrators which are symplectic-momentum preserving and are consistent with the jump conditions given in the continuous theory. Specific examples of these methods are tested numerically, and the long-time stable energy behavior typical of variational methods is demonstrated
Compliant contact force models in multibody dynamics : evolution of the Hertz contact theory
Over the last decades, several compliant contact force models have been proposed. However, no complete and systematic comparison has been done on these models, which provides information on their range of application and accuracy for use in different contact scenarios. Thus, the selection of an appropriate model for a given contact problem is still an important and challenging issue to be addressed. The Hertzian contact theory remains the foundation for almost all of the available force models, but by itself, it is not appropriate for most impacts in practice, due to the amount of energy dissipated during the impact. A good number of contact force models have been offered that augment the Hertzian law with a damping term to accommodate the energy loss during the impact process for small or moderate impact velocities. In this work, the main issues associated with the most common compliant contact force models of this type are analyzed. Results in terms of the dynamic simulations of multibody systems are presented, which allow for the comparison of the similarities and differences among the models considered.Fundação para a Ciência e a Tecnologia (FCT) - DACHOR - Multibody Dynamics and Control of
Hybrid Active Orthoses (MIT-Pt/BSHHMS/0042/2008), BIOJOINTS - Development of
advanced biological joint models for human locomotion biomechanics (PTDC/EMEPME/
099764/2008), SFRH/BD/40164/2007, SFRH/BD/64477/200
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Structure Preserving and Scalable Simulation of Colliding Systems
Predictive computational tools to study granular materials are important in fields ranging from the geosciences and civil engineering to computer graphics. The simulation of granular materials, however, presents many challenges. The behavior of a granular medium is fundamentally multi-scale, with pair-wise interactions between discrete granules able to influence the continuum-scale evolution of a bulk material. Computational techniques for studying granular materials must therefore contend with this multi-scale nature.
This research first addresses both the question of how to accurately model interactions between grains and the question of how to achieve multi-scale simulations of granular materials. We propose a novel rigid body contact model and a time integration technique that, for the first time, are able to simultaneously capture five key features of rigid body impact. We further validate this new model and time integration method by reproducing computationally challenging phenomena from granular physics.
We next propose a technique to couple discrete and continuum models of granular materials to one another. This hybrid model reveals a family of possible discretizations suitable for simulation. We derive an explicit integration technique from this framework that is able to capture phenomena previously reserved for discrete treatments, including frictional jamming, while treating bulk regions of the material with a continuum model. To effectively handle the large plastic deformations inherent in the evolution of a granular medium, we further propose a method to dynamically update which regions are treated with a discrete model and which regions are treated with a continuum model. We demonstrate that hybrid simulations of a dynamically evolving granular material are possible and practical, and lay the foundation for further algorithmic development in this space.
Finally, as the the tools used in computational science and engineering become progressively more complex, the ability to effectively train students in the field becomes increasingly important. We address the question of how to train students from a computer science background in numerical computation techniques by proposing a new system to automatically vet and identify problems in numerical simulations. This system has been deployed at the undergraduate and graduate level in a course on physical simulation at Columbia University, and has increased both student retention and student satisfaction with the course
Falling chains
The one-dimensional fall of a folded chain with one end suspended from a
rigid support and a chain falling from a resting heap on a table is studied.
Because their Lagrangians contain no explicit time dependence, the falling
chains are conservative systems. Their equations of motion are shown to contain
a term that enforces energy conservation when masses are transferred between
subchains. We show that Cayley's 1857 energy nonconserving solution for a chain
falling from a resting heap is incorrect because it neglects the energy gained
when a transferred link leaves a subchain. The maximum chain tension measured
by Calkin and March for the falling folded chain is given a simple if rough
interpretation. Other aspects of this falling folded chain are briefly
discussed.Comment: 9 pages, 1 figure; the Abstract has been shortened, three paragraphs
have been re-written for greater clarity, and textual improvements have been
made throughout the paper; to be published by the Am. J. Physic
On state and inertial parameter estimation of free-falling planar rigid bodies subject to unsche dule d frictional impacts
This paper addresses the problem of simultaneous state estimation and inertial and frictional parameter identification for planar rigid-bodies subject to unscheduled frictional impacts. The aim is to evaluate to what level of accuracy, given noisy captured poses of an object free-falling under gravity and impacting the surrounding environment, it is conceivable to reconstruct its states, the sequence of normal and tangential impulses and, concurrently, estimate its inertial properties along with Coulomb’s coefficient of friction at contacts.
To this aim we set up a constrained nonlinear optimization problem, where the unscheduled impacts are handled via a complementarity formulation. To assess the validity of the proposed approach we test the identification results both (i) with respect to ground truth values produced with a simulator, and (ii) with respect to real experimental data. In both cases, we are able to provide accurate/realistic estimates of the inertia-to-mass ratio and friction coefficient along with a satisfactory reconstruction of systems states and contact impulses
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