Skip to main content
SpringerLink
Log in

Dynamics of surface motion on a rotating massive homogeneous body

  • Article
  • Published:
Science China Physics, Mechanics and Astronomy Aims and scope Submit manuscript

Abstract

It is of great interest to study the dynamical environment on the surface of non-spherical small bodies, especially for asteroids. This paper takes a simple case of a cube for instance, investigates the dynamics of a particle on the surface of a rotating homogeneous cube, and derives fruitful results. Due to the symmetrical characteristic of the cube, the analysis includes motions on two different types of surfaces. For each surface, both the frictionless and friction cases are considered. (i) Without consideration of friction, the surface equilibria in both of the different surfaces are examined and periodic orbits are derived. The analysis of equilibria and periodic orbits could assist understanding the skeleton of motions on the surface of asteroids. (ii) For the friction cases, the conditions that the particle does not escape from the surface are examined. Due to the effect of the friction, there exist the equilibrium regions on the surface where the particle stays at rest, and the locations of them are found. Finally, the dust collection regions are predicted. Future work will extend to real asteroid shapes.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Scheeres D J, Ostro S J, Hudson R S, et al. Orbits close to asteroid 4769 Castalia. Icarus, 1996, 121: 67–87

    Article  ADS  Google Scholar 

  2. Scheeres D J, Ostro S J, Hudson R S, et al. Dynamics of orbits close to asteroid 4179 Toutatis. Icarus, 1998, 132: 53–79

    Article  ADS  Google Scholar 

  3. Hudson R S, Ostro S J, Jurgens R F, et al. Radar observations and physical model of asteroid 6489 Golevka. Icarus, 2000, 148: 37–51

    Article  ADS  Google Scholar 

  4. Scheeres D J, Gaskell R, Abe S, et al. The actual dynamical environment about Itokawa. In: Proceedings of AIAA/AAS Astrodynamics Specialist Conference and Exhibit. Keystone: AIAA, 2006

    Google Scholar 

  5. Magri C, Ostro S J, Scheeres D J, et al. Radar observations and a physical model of asteroid 1580 Betulia. Icarus, 2007, 186: 152–177

    Article  ADS  Google Scholar 

  6. Shepard M K, Clark B E, Nolan M C, et al. Multi-wavelength observations of asteroid 2100 Ra-Shalom. Icarus, 2008, 193: 20–38

    Article  ADS  Google Scholar 

  7. Brozovic M, Ostro S J, Benner L A M, et al. Radar observations and a physical model of asteroid 4660 Nereus: A prime space mission target. Icarus, 2009, 201: 153–166

    Article  ADS  Google Scholar 

  8. Sawai S, Kawaguchi J, Scheeres D J. et al. Development of a target marker for landing on asteroids. J Spacecr Rocket, 2001, 38: 601–608

    Article  Google Scholar 

  9. Scheeres D J, Durda D D, Geissler P E. The fate of asteroid ejecta. In: Bottke W F, Cellino A, Paolicchi P, et al. eds. Asteroids III. Tucson: University of Arizona Press, 2002. 527–544

    Google Scholar 

  10. Scheeres D J, Hartzell C M, Sanchez P, et al. Scaling forces to asteroid surfaces: The role of cohesion. Icarus, 2010, 210: 968–984

    Article  ADS  Google Scholar 

  11. Guibout V, Scheeres D J. Stability of surface motion on a rotating ellipsoid. Celest Mech Dyn Astron, 2003, 87: 263–290

    Article  ADS  MATH  MathSciNet  Google Scholar 

  12. Bellerose J, Scheeres D J. Dynamics and control for surface exploration of small bodies. In: Proceedings of AIAA/AAS Astrodynamics Specialist Conference and Exhibit. Honolulu: AIAA, 2008

    Google Scholar 

  13. Bellerose J, Girard A, Scheeres D J. Dynamics and control of surface exploration robots on asteroids. In: Hirsch M J, Commander C, Pardalos PM, et al. eds. Optimization and Cooperative Control Strategies. Gainesville: Springer, 2009. 135–150

    Chapter  Google Scholar 

  14. Antreasian P G, Chesley S R, Miller J K, et al. The design and navigation of the near-shoemaker landing on Eros. In: Proceedings of AAS/AIAA Astrodynamics Specialist Conference. Quebec City: AAS Publications, 2001

    Google Scholar 

  15. Yano H, Kubota T, Miyamoto H. Touchdown of the Hayabusa spacecraft at the Muses Sea on Itokawa. Science, 2006, 312: 1350–1353

    Article  ADS  Google Scholar 

  16. Ronca L B, Furlong R B. The shape of asteroids: Theoretical considerations. Earth Moon Planets, 1979, 21: 409–417

    Article  MATH  Google Scholar 

  17. Werner R A. The gravitational potential of a homogeneous polyhedron or don’t cut corners. Celest Mech Dyn Astron, 1994, 59: 253–278

    Article  ADS  MATH  Google Scholar 

  18. Riaguas A, Elipe A, Lara M. Periodic orbits around a massive straight segment. Celest Mech Dyn Astron, 1999, 73: 169–178

    Article  ADS  MATH  MathSciNet  Google Scholar 

  19. Arribas M, Elipe A. Non-integrability of the motion of a particle around a massive straight segment. Phys Lett A, 2001, 281: 142–148

    Article  ADS  MATH  MathSciNet  Google Scholar 

  20. Riaguas A, Elipe A, López-Moratalla T. Non-linear stability of the equilibria in the gravity field of a finite straight segment. Celest Mech Dyn Astron, 2001, 81: 235–248

    Article  ADS  MATH  Google Scholar 

  21. Elipe A, Riaguas A. Nonlinear stability under a logarithmic gravity field. Int Math J, 2003, 3: 435–453

    MATH  MathSciNet  Google Scholar 

  22. Gutiérrez-Romero S, Palacián J F, Yanguas P. The invariant manifolds of a finite straight segment. Monografías de la Real Academia de Ciencias de Zaragoza, 2004, 25: 137–148

    Google Scholar 

  23. Palacián J F, Yanguas P, Gutiérrez-Romero S. Approximating the invariant sets of a finite straight segment near its collinear equilibria. SIAM J Appl Dyn Syst, 2006, 5: 12–29

    Article  MATH  MathSciNet  Google Scholar 

  24. Broucke R A, Elipe A. The dynamics of orbits in a potential field of a solid circular ring. Regul Chaotic Dyn, 2005, 10: 129–143

    Article  ADS  MATH  MathSciNet  Google Scholar 

  25. Azevêdo C, Cabral H E, Ontaneda P. On the fixed homogeneous circle problem. Adv Nonlinear Stud, 2007, 7: 47–75

    MATH  MathSciNet  Google Scholar 

  26. Azevêdo C, Ontaneda P. On the existence of periodic orbits for the fixed homogeneous circle problem. J Differ Equ, 2007, 235: 341–365

    Article  MATH  Google Scholar 

  27. Fukushima T. Precise computation of acceleration due to uniform ring or disk. Celest Mech Dyn Astron, 2010, 108: 339–356

    Article  ADS  MATH  MathSciNet  Google Scholar 

  28. Alberti A, Vidal C. Dynamics of a particle in a gravitational field of a homogeneous annulus disk. Celest Mech Dyn Astron, 2007, 98: 75–93

    Article  ADS  MATH  MathSciNet  Google Scholar 

  29. Blesa F. Periodic orbits around simple shaped bodies. Monografías del Seminario Matemático García de Galdeano, 2006, 33: 67–74

    MathSciNet  Google Scholar 

  30. Michalodimitrakis M, Bozis G. Bounded motion in a generalized two-body problem. Astrophys Space Sci, 1985, 117: 217–225

    Article  ADS  MATH  MathSciNet  Google Scholar 

  31. 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, 1997, 65: 313–344

    Article  ADS  MATH  Google Scholar 

  32. Thomas P C. Gravity, tides, and topography on small satellites and asteroids: Application to surface features of the martian satellites. Icarus, 1993, 105: 326–344

    Article  ADS  Google Scholar 

  33. Robinson R C. An Introduction to Dynamical Systems: Continuous and Discrete. Upper Saddle River, NJ: Pearson Prentice Hall, 2004

    MATH  Google Scholar 

  34. Robinson M S, Thomas P C, Veverka J, et al. The nature of ponded deposits on Eros. Nature, 2001, 413: 396–400

    Article  ADS  Google Scholar 

  35. Ostro S J, Margot J-L, Benner L A M, et al. Radar imaging of binary near-Earth asteroid (66391) 1999 KW4. Science, 2006, 314: 1276–1280

    Article  ADS  Google Scholar 

  36. Miyamoto H, Yano H, Scheeres D J, et al. Regolith migration and sorting on asteroid Itokawa. Science, 2007, 316: 1011–1014

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Aerospace, Tsinghua University, Beijing, 100084, China

    XiaoDong Liu, HeXi Baoyin & XingRui Ma

Authors
  1. XiaoDong Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. HeXi Baoyin
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. XingRui Ma
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to HeXi Baoyin.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Liu, X., Baoyin, H. & Ma, X. Dynamics of surface motion on a rotating massive homogeneous body. Sci. China Phys. Mech. Astron. 56, 818–829 (2013). https://doi.org/10.1007/s11433-013-5044-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11433-013-5044-2

Keywords

Search

Navigation