\(N\)-body gravitational and contact dynamics for asteroid aggregation. (English) Zbl 1404.70031
Summary: The development of dedicated numerical codes has recently pushed forward the study of \(N\)-body gravitational dynamics, leading to a better and wider understanding of processes involving the formation of natural bodies in the Solar System. A major branch includes the study of asteroid formation: evidence from recent studies and observations support the idea that small and medium size asteroids between 100 m and 100 km may be gravitational aggregates with no cohesive force other than gravity. This evidence implies that asteroid formation depends on gravitational interactions between different boulders and that asteroid aggregation processes can be naturally modeled with \(N\)-body numerical codes implementing gravitational interactions. This work presents a new implementation of an \(N\)-body numerical solver. The code is based on Chrono::Engine (2006). It handles the contact and collision of large numbers of complex-shaped objects, while simultaneously evaluating the effect of \(N\) to \(N\) gravitational interactions. A special case of study is considered, investigating the relative dynamics between the \(N\) bodies and highlighting favorable conditions for the formation of a stable gravitationally bound aggregate from a cloud of \(N\) boulders. The code is successfully validated for the case of study by comparing relevant results obtained for typical known dynamical scenarios. The outcome of the numerical simulations shows good agreement with theory and observation, and suggests the ability of the developed code to predict natural aggregation phenomena.
Keywords:
\(N\)-body problem; asteroid aggregation; contact dynamics; rigid body; non-spherical shapeReferences:
| [1] | Tasora, A., Negrut, D., Serban, R., Mazhar, H., Heyn, T., Pazouki, A., Melanz, D.: Chrono::engine web pages at projectchrono.org (2006) · Zbl 0881.70008 |
| [2] | Biele, J., Ulamec, S.: Capabilities of Philae, the Rosetta lander. Space Sci. Rev. 138, 275-289 (2008) · doi:10.1007/s11214-007-9278-z |
| [3] | Heggy, E., Palmer, E.M., Kofman, W., Clifford, S.M., Righter, K., Hérique, A.: Radar properties of comets: parametric dielectric modeling of comet 67p/Churyumov-Gerasimenko. Icarus 221, 925-939 (2012) · doi:10.1016/j.icarus.2012.09.023 |
| [4] | Kaula, W.M.: Theory of Satellite Geodesy. Blaisdell, Waltham (1966) · Zbl 0973.86001 |
| [5] | Scheeres, D.J.: Dynamics about uniformly rotating triaxial ellipsoids: applications to asteroids. Icarus 110, 225-238 (1994) · doi:10.1006/icar.1994.1118 |
| [6] | Werner, R.A., Scheeres, D.J.: Exterior gravitation of a polyhedron derived and compared with harmonic and mascon gravitation representations of asteroid 4769 Castalia. Celest. Mech. Dyn. Astron. 65, 313-344 (1997) · Zbl 0881.70008 · doi:10.1007/BF00053511 |
| [7] | Scheeres, D.J., Ostro, S.J., Hudson, R.S., DeJong, E.M., Suzuki, S.: Dynamics of orbits close to asteroid 4179 Toutatis. Icarus 132, 53-79 (1998) · doi:10.1006/icar.1997.5870 |
| [8] | Chapman, C. R., Asteroid collisions, craters, regolith and lifetimes, No. 2053, 145-160 (1978) |
| [9] | Richardson, D. C.; Leinhardt, Z. M.; Melosh, H. J.; Bottke, W. F.; Asphaug, E., Gravitational aggregates: evidence and evolution, 501-515 (2002), Tucson |
| [10] | Morbidelli, A.: Modern integrations of solar system dynamics. Annu. Rev. Earth Planet. Sci. 30 (2002) · Zbl 1411.70019 |
| [11] | Stadel, J.: Cosmological \(NN\)-body simulations and their analysis. PhD thesis, University of Washington, Seattle, WA, USA (2001) · Zbl 1333.68258 |
| [12] | Richardson, D.C., Quinn, T., Stadel, J., Lake, G.: Direct large-scale n \(n\)-body simulations of planetesimal dynamics. Icarus 143, 45-59 (2000) · doi:10.1006/icar.1999.6243 |
| [13] | Richardson, D.C., Michel, P., Walsh, K.J., Flynn, K.W.: Numerical simulations of asteroids modelled as gravitational aggregates. Planet. Space Sci. 57, 183-192 (2009) · doi:10.1016/j.pss.2008.04.015 |
| [14] | Aarseth, S.J.: Nbody2: a direct n \(n\)-body integration code. New Astron. 6, 277-291 (2001) · doi:10.1016/S1384-1076(01)00060-4 |
| [15] | Pruett, C.D., Rudmin, J.W., Lacy, J.M.: An adaptive n \(n\)-body algorithm of optimal order. J. Comput. Phys. 187, 298-317 (2003) · Zbl 1047.70002 · doi:10.1016/S0021-9991(03)00101-3 |
| [16] | Dorband, E.N., Hemsendorf, M., Merritt, D.: Systolic and hyper-systolic algorithms for the gravitational n \(n\)-body problem, with an application to Brownian motion. J. Comput. Phys. 185, 484-511 (2003) · Zbl 1015.83004 · doi:10.1016/S0021-9991(02)00067-0 |
| [17] | Wisdom, J., Holman, M.: Symplectic maps for the n \(n\)-body problem. Astron. J. 102, 1528-1538 (1991) · doi:10.1086/115978 |
| [18] | Duncan, M.J., Levison, H.F., Lee, M.H.: A multiple time step symplectic algorithm for integrating close encounters. Astron. J. 116, 2067-2077 (1998) · doi:10.1086/300541 |
| [19] | Chambers, J.E.: A hybrid symplectic integrator that permits close encounters between massive bodies. Mon. Not. R. Astron. Soc. 304, 793-799 (1999) · doi:10.1046/j.1365-8711.1999.02379.x |
| [20] | Michel, P., Tanga, P., Benz, W., Richardson, D.C.: Formation of asteroid families by catastrophic disruption: simulations with fragmentation and gravitational reaccumulation. Icarus 160, 10-23 (2002) · doi:10.1006/icar.2002.6948 |
| [21] | Mazhar, H., Heyn, T., Pazouki, A., Melanz, D., Seidl, A., Barthlomew, A., Tasora, A., Negrut, D.: Chrono: a parallel multi-physics library for rigid-body, flexible-body and fluid dynamics. Mech. Sci. (2013) |
| [22] | Anitescu, M., Tasora, A.: An iterative approach for cone complementarity problems for nonsmooth dynamics. Comput. Optim. Appl. 47(2), 207-235 (2010) · Zbl 1200.90160 · doi:10.1007/s10589-008-9223-4 |
| [23] | Moreau, J.J.: Numerical aspects of the sweeping process. Comput. Methods Appl. Mech. Eng. 177(3-4), 329-349 (1999) · Zbl 0968.70006 · doi:10.1016/S0045-7825(98)00387-9 |
| [24] | Stewart, D.E., Trinkle, J.C.: An implicit time-stepping scheme for rigid body dynamics with inelastic collisions and Coulomb friction. Int. J. Numer. Methods Eng. 39(15), 281-287 (1996) · Zbl 0882.70003 · doi:10.1002/(SICI)1097-0207(19960815)39:15<2673::AID-NME972>3.0.CO;2-I |
| [25] | Potra, F.A., Anitescu, M., Gavrea, B., Trinkle, J.: A linearly implicit trapezoidal method for integrating stiff multibody dynamics with contact and friction. Int. J. Numer. Methods Eng. 66(7), 1079-1124 (2006) · Zbl 1110.70303 · doi:10.1002/nme.1582 |
| [26] | Renouf, M., Alart, P.: Conjugate gradient type algorithms for frictional multi-contact problems: applications to granular materials. Comput. Methods Appl. Mech. Eng. 194(18-20), 2019-2041 (2005) · Zbl 1091.74053 · doi:10.1016/j.cma.2004.07.009 |
| [27] | Leine, R., Glocker, C.: A set-valued force law for spatial Coulomb-Contensou friction. Eur. J. Mech. 22(2), 193-216 (2003) · Zbl 1038.74513 · doi:10.1016/S0997-7538(03)00025-1 |
| [28] | Acary, V.; Brogliato, B., Numerical methods for nonsmooth dynamical systems: applications in mechanics and electronics, No. 35 (2008), Berlin · Zbl 1173.74001 |
| [29] | Tasora, A., Anitescu, M.: A complementarity-based rolling friction model for rigid contacts. Meccanica 48(7), 1643-1659 (2013) · Zbl 1293.70052 · doi:10.1007/s11012-013-9694-y |
| [30] | Pang, J.S., Stewart, D.E.: Differential variational inequalities. Math. Program. 113, 1-80 (2008) · Zbl 1139.58011 · doi:10.1007/s10107-006-0052-x |
| [31] | De Saxcé, G., Feng, Z.-Q.: Recent advances in contact mechanics the bipotential method: a constructive approach to design the complete contact law with friction and improved numerical algorithms. Math. Comput. Model. 28(4), 225-245 (1998) · Zbl 1126.74341 · doi:10.1016/S0895-7177(98)00119-8 |
| [32] | Pfeiffer, F., Glocker, C.: Multibody Dynamics with Unilateral Contacts. Wiley, New York (1996) · Zbl 0922.70001 · doi:10.1002/9783527618385 |
| [33] | Heyn, T., Anitescu, M., Tasora, A., Negrut, D.: Using Krylov subspace and spectral methods for solving complementarity problems in many-body contact dynamics simulation. Int. J. Numer. Methods Eng. 95(7), 541-561 (2013) · Zbl 1352.74206 · doi:10.1002/nme.4513 |
| [34] | Mazhar, H., Heyn, T., Negrut, D., Tasora, A.: Using Nesterov’s method to accelerate multibody dynamics with friction and contact. ACM Trans. Graph. 34(3), 32:1-32:14 (2015) · Zbl 1333.68258 · doi:10.1145/2735627 |
| [35] | Munthe-Kaas, H.: High order Runge-Kutta methods on manifolds. Appl. Numer. Math. 29(1), 115-127 (1999). Proceedings of the NSF/CBMS Regional Conference on Numerical Analysis of Hamiltonian Differential Equations · Zbl 0934.65077 · doi:10.1016/S0168-9274(98)00030-0 |
| [36] | Terze, Z., Müller, A., Zlatar, D.: Singularity-free time integration of rotational quaternions using non-redundant ordinary differential equations. Multibody Syst. Dyn., 1-25 (2016) · Zbl 1386.70009 |
| [37] | Tasora, A., Anitescu, M.: A matrix-free cone complementarity approach for solving large-scale, nonsmooth, rigid body dynamics. Comput. Methods Appl. Mech. Eng. 200, 439-453 (2011) · Zbl 1225.70004 · doi:10.1016/j.cma.2010.06.030 |
| [38] | Tasora, A., Negrut, D., Anitescu, M.: Large-scale parallel multi-body dynamics with frictional contact on the graphical processing unit. J. Multi-Body Dyn. 222, 315-326 (2008) |
| [39] | Tasora, A., Anitescu, M.: A convex complementarity approach for simulating large granular flows. J. Comput. Nonlinear Dyn. 5, 1-10 (2010) · Zbl 1200.90160 |
| [40] | Bradford Barber, C., Dobkin, D.P., Huhdanpaa, H.: The quickhull algorithm for convex hulls. ACM Trans. Math. Softw. 22(4), 469-483 (1996) · Zbl 0884.65145 · doi:10.1145/235815.235821 |
| [41] | Keerthi, S.S., Gilbert, E.G., Johnson, D.W.: A fast procedure for computing the distance between complex objects in three-dimensional space. Robot. Autom. 4(2), 193-203 (1988) · doi:10.1016/0921-8890(88)90025-5 |
| [42] | Johnston, R.: Johnston’s archive web pages at johnstonsarchive.net (2016) · Zbl 0806.68107 |
| [43] | NASA, J.P.L.: Jpl small-body database web pages at ssd.jpl.nasa.gov (2016) · Zbl 1333.68258 |
| [44] | Edelsbrunner, H., Mücke, E.P.: Three-dimensional alpha shapes. Trans. Graph. 13(1), 43-72 (1994) · Zbl 0806.68107 · doi:10.1145/174462.156635 |
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