Abstract
In this chapter we study the dynamics of a freely rotating rubble asteroid employing volume-averaged equations developed in Chap. 3. Our mainly analytical approach provides an alternative to more computationally intensive paradigms, e.g., discrete element simulations, with which we compare our predictions. These results have implications on rotation-driven disruption of rubble-piles, as well as, re-aggregation processes.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
Simple, at least when compared with the non-linear partial differential equations governing elasto-plasto-dynamics!.
- 2.
It is unclear when, and under what conditions, does the angle of repose equal the results of triaxial or shear-box tests, although simplified analyses predict that they will be closely related; see, e.g., Nedderman (1992, Sect. 3.5).
- 3.
Hard spheres rolling without slipping on a plane come to a stop in spite of rigid body mechanics predicting eternal motion. This is attributed to the hard sphere deforming locally around the contact point leading to contact over a region. Microslipping and asymmetric pressure distribution within the contact region then lead to the sphere experiencing a net retarding force and a macroscopic torque about its mass center that make it stop. This is called rolling resistance; see, e.g., Johnson (1985, p. 306) for more details.
- 4.
A general planar flyby of a granular asteroid is explored in Chap. 12.
References
S. Baghel, Internal Friction in Virtual Soils Employed in Discrete Element Simulations. Master’s thesis, Indian Institute of Technology Kanpur (2015)
M.D. Bolton, A Guide to Soil Mechanics, 3rd edn. (Universities Press, Hyderabad, 2003)
S. Chandrasekhar, Ellipsoidal Figures of Equilibrium (Yale University Press, New Haven, 1969)
P.A. Cundall, O.D.L. Strack, A discrete numerical model for granular assemblies. Géotechnique 29, 47–65 (1979)
K.A. Holsapple, Equilibrium configurations of solid cohesionless bodies. Icarus 154, 432–448 (2001)
K.A. Holsapple, Equilibrium figures of spinning bodies with self-gravity. Icarus 172, 272–303 (2004)
K.A. Holsapple, On YORP-induced spin deformations of asteroids. Icarus 205, 430–442 (2010)
K.L. Johnson, Contact Mechanics, 3rd edn. (Cambridge University Press, Cambridge, 1985)
P. Michel, W. Benz, D.C. Richardson, Collisions and gravitational reaccumulation: forming asteroid families and satellites. Science 294, 1696–1700 (2001)
R.M. Nedderman, Statics and Kinematics of Granular Materials (Cambridge University Press, Cambridge, 1992)
H. Pawar, Interaction Laws in Discrete Element Method. Master’s thesis, Indian Institute of Technology Kanpur (2013)
D.C. Richardson, W.F. Bottke Jr., S.G. Love, Tidal distortion and disruption of earthcrossing asteroids. Icarus 134, 47–76 (1998)
D.C. Richardson, P. Elankumaran, R.E. Sanderson, Numerical experiments with rubble piles: Equilibrium shapes and spins. Icarus 173, 349–361 (2005)
P. Sanchez, D.J. Scheeres, Simulating asteroid rubble piles with a self-gravitating softsphere distinct element method model. Astrophys. J. 727, 120–133 (2011)
P. Sanchez, D.J. Scheeres, DEM simulation of rotation-induced reshaping and disruption of rubble-pile asteroids. Icarus 218, 876–894 (2012)
D.J. Scheeres, S.J. Ostro, R.A. Werner, E. Asphaug, R.S. Hudson, Effect of gravitational interactions on asteroid spin states. Icarus 147, 106–118 (2000)
D.J. Scheeres, L.A.M. Benner, S.J. Ostro, A. Rossi, F. Mazari, P. Washabaugh, Abrupt alteration of asteroid 2004 MN4’s spin state during its 2029 earth flyby. Icarus 178, 281–283 (2005)
I. Sharma, J.T. Jenkins, J.A. Burns, Dynamical passage to approximate equilibrium shapes for spinning, gravitating rubble asteroids. Icarus 200, 304–322 (2009)
J.C. Simo, T.J.R. Hughes, Computational Inelasticity (Springer, New York, 1997)
K.J. Walsh, D.C. Richardson, P. Michel, Rotational breakup as the origin of small binary asteroids. Nature 454, 188–191 (2008)
S.J. Weidenschilling, Initial sizes of planetesimals and accretion of the asteroids. Icarus 214, 671–684 (2011)
Y.C. Zhou, B.D. Wright, R.Y. Yang, B.H. Xu, A.B. Yu, Rolling friction in the dynamic simulation of sandpile formation. Phys. A 269, 536–553 (1999)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2017 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Sharma, I. (2017). Formation. In: Shapes and Dynamics of Granular Minor Planets. Advances in Geophysical and Environmental Mechanics and Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-319-40490-5_11
Download citation
DOI: https://doi.org/10.1007/978-3-319-40490-5_11
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-40489-9
Online ISBN: 978-3-319-40490-5
eBook Packages: Earth and Environmental ScienceEarth and Environmental Science (R0)