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A Perspective on Computer-Oriented Mutlibody Dynamical Formalisms and their Implementations

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Dynamics of Multibody Systems

Part of the book series: IUTAM Symposium ((IUTAM))

Abstract

Past work on computer-oriented formalisms for rigid/gyrostatic bodies is surveyed, together with their numerical computer program implementations.

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References

  1. Amin, A., “Automatic formulation and solution techniques in dynamics of machinery”, Ph.D. dissertation, University of Pennsylvania, Philadelphia, 1979.

    Google Scholar 

  2. Andrews, G.C., “The vector-network model: a topological approach to mechanics”, Ph.D. dissertation, University of Waterloo, 1971.

    Google Scholar 

  3. Andrews, G.C., Kesavan, H.K., “The vector-network model: a new approach to vector dynamics”, Mechanism and Machine Th. 10 (1975), 57–75.

    Article  Google Scholar 

  4. Andrews, G.C., Kesavan, H.K., “Simulation of multibody systems using the vector-network model”, Dynamics of Multibody Systems, Proc. IUTAM Symposium. (Munich, 1977), K. Magnus ed., Springer, Berlin, 1978, pp. 1–13.

    Google Scholar 

  5. Bayazitoglu, Y.O., Methods for automated analysis of three-dimensional mechanical dynamic systems with application to nonlinear vehicle dynamics“, Ph.D. dissertation,;University of Michigan, 1972.

    Google Scholar 

  6. Chace, M.A., “Analysis of time-dependent of multi-freedom mechanical systems in relative coordinates”, J. Engrg. Ind. 89 (1967), 119–125.

    Article  Google Scholar 

  7. Chace, M.A., “Methods and experience in computer aided design of large-displacement mechanical systems”, NATO Advanced Study Inst. on Computer Aided Analysis and Optimization of Mechanical System Dynamics, J. Haug, ed., Springer, Berlin, 1984, pp. 233–259.

    Google Scholar 

  8. Chace, M.A., Angell, J.C., “Interactive simulation of machinery with friction and impact using Dram”, Trans. SAE 86 (1977), 239–250. (Paper 770050)

    Google Scholar 

  9. Chace, M.A., Bayazitoglu, Y.O., “Development and application of a generalized d’Alembert force for multifreedom mechanical systems”, J. Engrg. Ind. 93 (1971), 317–327.

    Article  Google Scholar 

  10. Chace, M.A., Sheth, P.N., “Adaptation of computer techniques to the design of mechanical dynamic machinery”, ASME Paper 73-DET-58, ASME, NY, 1973.

    Google Scholar 

  11. Chace, M.A., Smith, D.A., “DAMN–digital computer programn for the dynamic analysis of generalized mechanical systems”, Trans. SAE 80 (1971), 969–983.

    Google Scholar 

  12. Dix, R.C., Lehman, T.J., “Simulation of the dynamics of machinery”, J. Engrg. Ind. 94 (1972), 433–938.

    Article  Google Scholar 

  13. Fleischer, G.E., “Multi-rigid-body attitude dynamics simulation”, JPL Tech. Report 32–1516, Pasadena, 1971.

    Google Scholar 

  14. Fleischer, G.C., Likins, P.W., “Attitude dynamics simulation subroutines for systems of hinge-connected rigid bodies”, JPL Tech. Report 32–1592, Pasadena, 1974.

    Google Scholar 

  15. Fletcher, H.J., Rongved, L., Yu, E.Y., “Dynamics analysis of a two-body gravitationally oriented satellite”, Bell System Tech. J 42 # 5 (1963), 2239–2266.

    Google Scholar 

  16. Frisch, H.P., “A vector-dyadic development of the equations of motion for N-coupled rigid bodies and point masses”, NASA TN D-7767, 1974.

    Google Scholar 

  17. Frisch, H.P., “The N-BOD2 User’s and Programmer’s Manual”, NASA Tech. Paper 1145, 1978.

    Google Scholar 

  18. Hooker, W.W., “Equations of motion for interconnected rigid and elastic bodies: a derivation independent of angular momentum”, Celestial Mech. 2 (1975), 337–359.

    Article  MathSciNet  ADS  Google Scholar 

  19. Hooker, W.W., Margulies, G., “The dynamical attitude equations for n-body satellite”, J. Astronautical Sci. 12 (1965), 123–128.

    MathSciNet  ADS  Google Scholar 

  20. Hooker, W.W., “A set of r dynamical attitude equations for an arbitrary n-body satellite having r rotational degrees of freedom”, AIAA J 8 # 7 (1970), 1205–1207.

    Article  ADS  MATH  Google Scholar 

  21. Huston, R.L., Passejello, C.E., “On multi-rigid-body system dynamics”, Computers and Structures 10 (1979), 439–496.

    Article  ADS  MATH  Google Scholar 

  22. Huston, R.L., Passerello, C.E., “Multibody structural dynamics including translation between bodies”, Computers and Structures 12 (1980). 713–720.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  23. Huston, R.L., Passerello, C.E., Harlow, M.W., “Dynamics of multirigid-body systems”, J. Appl. Mech 45 (1978), 889–894.

    Article  ADS  Google Scholar 

  24. Jerkovsky, W., “The structure of multi-body dynamics equations”, Proc. Sympos. Dynamics and Control of Large Flexible Structures (Blacksburg VA, 1977), pp.387–421. Also J. Guidance and Control 1 (1978), 173–182.)

    Google Scholar 

  25. Kamman, J.W., Huston, R.L., “Dynamics of constrained multibody systems”, J. Appl. Mech. 51 (1984), 899–903.

    Article  ADS  MATH  Google Scholar 

  26. Kane, T.R., “Dynamics of nonholonomic systems”, J. Appl. Mech. 28 (1961), 574–578.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  27. Kane, T.R., Levinson, A.D., “Formulation of equations of motion for complex spacecraft”, J. Guidance Control 3 (1980), 99–112.

    Article  MathSciNet  MATH  Google Scholar 

  28. Kane, T.R., Wang, C.F., “On the derivation of equations of motion”, J. Soc. Ind. Appl. Math. 13 (1965), 987–992.

    Article  MathSciNet  Google Scholar 

  29. Likins, P.W., “Point-connected rigid bodies in a topological tree”, Celestial Mechanics 11 (1975), 301–317.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  30. Lilov, L., Lorer, M., “Dynamic analysis of multirigid-body system based on the Gauss principle”, ZAMM 62 (1982), 539–545.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  31. Lilov, L., Wittenburg, J., “Bewegungsgleichungen für Systeme starrer Körper mit Gelenken beliebiger Eigenschaften”, ZAMM 57 (1977), 137–152.

    Article  MATH  Google Scholar 

  32. Maros, D., Orlandea, N., “Contributions to the determination of the equations of motion for multidegree of freedom systems”, J. Engrg. hid. 93 (1971), 191–195.

    Google Scholar 

  33. Ness, D.J., Farrenkopf, R.L., “Inductive methods for generating the dynamic equations of motion for multibodied flexible systems”, ASME, NY, 1971.

    Google Scholar 

  34. Nikravesh, P.E., Chung, I.S., “Application of Euler parameters to the dynamic analysis of three-dimensional systems with nonholonomic constraints”, J. Mech. Design 104 (1982), 785–791.

    Article  Google Scholar 

  35. Nikravesh, P.E., Haug, E.J., “Generalized coordinate partitioning for analysis of mechanical systems with nonholonomic constraints”, J. Mechanisms, Transmissions Automation in Design 105 (1983), 379–384.

    Article  Google Scholar 

  36. Orlandea, N., “Node-analogous, sparsity-oriented methods for simulation of mechanical systems”, Ph.D. dissertation, University of Michigan, 1973.

    Google Scholar 

  37. Orlandea, N., Chace, M.A., Calahan, D.A., “A sparsity-oriented approach to the dynamic analysis and design of mechanical systems–Part 1”, J. Engrg. Ind. 99 (1977), 773–784.

    Article  Google Scholar 

  38. Paul, B., “Analytical dynamics of mechanisms–a computer oriented overview”, Mechanism and Machine Theory 10 (1975), 481–507.

    Article  Google Scholar 

  39. Paul, B., “Dynamic analysis of machinery via program DYMAC”, SAE Paper 770049, Soc. of Automotive Engrs., 1977.

    Google Scholar 

  40. Paul, B., Kinematics and Dynamics of Planar Machinery, Prentice Hall, Englewood Cliffs, NJ, 1979, Part 2.

    Google Scholar 

  41. Paul, B., “Computer oriented analytical dynamics of machinery”, NATO Advanced Study Inst. on Computer Aided Analysis and Optimization of Mechanical System Dynamics, (Iowa City, 1983), E.J. Haug, ed., Springer, Berlin, 1984, pp. 41–87.

    Google Scholar 

  42. Paul, R.P., Robot manipulators: Mathematics, programming and control, MIT Press, Cambridge, 1981.

    Google Scholar 

  43. Roberson, R.E., “A form of the translational dynamical equations for relative motion in systems of many nonrigid bodies”, Acta Mechanics 14 (1972), 297–308.

    Article  MATH  Google Scholar 

  44. Roberson, R.E., “Computer-oriented dynamical modelling of spacecraft: historical evolution of Eulerian multi-body formalisms since 1750”, Proc. 28th Int. Astronaut. Congr. (Prag, 1977), IAF Paper 77-All.

    Google Scholar 

  45. Roberson, R.E., Duo Ti Xi Tong Dong Li Xue (Dynamics of Multibody Systems), Lectures given at the Nanjing Aeronautical Institute, 5–16 September 1983, Nanjing Aeronautical Institute, Sep 1984. (Chinese)

    Google Scholar 

  46. Roberson, R.E., Wittenburg, J., “A dynamical formalisms for an arbitrary number of interconnected rigid bodies, with reference to the problem of satellite attitude control”, Proc. 3rd Congr. Int. Fed. Auto. Control (London, 1966 ); Vol.1 Book 3 System Dynamics, Butterworth, London, undated, Paper 46D.

    Google Scholar 

  47. Rogers, R.J., Andrews, G.C., “Simulating planar systems using a simplified vector-network method”, Mechanism and Machine Th. 10 (1975), 509–519.

    Article  Google Scholar 

  48. Savage, G.J., Andrews, G.C., “DYNIS: a dynamic interactive simulation program for three-dimensional mechanical systems”, Proc. 3rd man-computer communications seminar, (Ottawa, 1973 ).

    Google Scholar 

  49. Schiehlen, W.O., “Dynamics of complex multibody systems”, SM Archives 9 (1984), 159–195.

    MATH  Google Scholar 

  50. Schiehlen, W.O., “Computer generation of equations of motion”, NATO Advanced Study Inst. on Computer Aided Analysis and Optimization of Mechanical System Dynamics, E.J. Haug, ed., Springer, Berlin, 1984, pp. 183–215.

    Google Scholar 

  51. Schiehlen, W.O., Kreuzer, E.J., “Rechnergestützes Aufstellen der Bewegungsgleichungen gewöhnlicher Mehrkörpersysteme”, Ing.-Archiv 46 (1977), 185–194.

    Article  MATH  Google Scholar 

  52. Schwertassek, R., “Der Roberson/Wittenburg-Formalismus and das Programmsystem MULTIBODY zur Rechnersimulation von Mehrkörpersystemen.” Report DFVLR-FB-78/08, DFVLR, Wissenschaftliches Berichtswesen, Köln, 1978.

    Google Scholar 

  53. Schwertassek, R., Roberson, R.E., “A state-space dynamical representation for multibody mechanical systems. Part I: Systems with tree configuration”, Acta Mechanics 50 (1983), 141–161.

    Article  ADS  Google Scholar 

  54. Schwertassek, R., Roberson, R.E., “Part H: Systems with closed loops”, Acta Méchanica 51 (1984), 15–29.

    Article  ADS  MATH  Google Scholar 

  55. Sheth, P.N., “A digital computer based simulation procedure for multiple degree of freedom mechanical systems with geometric constraints”, PhD. dissertation, University of Wisconsin, 1972.

    Google Scholar 

  56. Sheth, P.N., Uicker, J.J., “IMP (integrated mechanism program), a computer-aided design analysis system for mechanisms and linkage”, J. Engrg. Ind. 94 (1972), 454–464.

    Article  Google Scholar 

  57. Velman, J.R., “Simulation results for a dual-spin spacecraft”, Proc. Sympos. Attitude Stabilization and Control of Dual-Spin Spacecraft, (El Segundo CA, Dec 1967), SAMSO-TR-68–191, Air Force Systems Command, Space and Missile Systems Organization, pp. 11–23.

    Google Scholar 

  58. Wittenburg, J., “The dynamics of systems of coupled rigid bodies. A new general formalism with applications” Stereodynamics Centro Internazionale Matematico Estivo, I Ciclo 1971 (Bressanone, 2–12 Jun 1971), Edizioni Cremonese, Roma, 1972.

    Google Scholar 

  59. Wittenburg, J., “Nonlinear equations of motion for arbitrary systems of interconnected rigid bodies”, Dynamics of Multibody Systems, Proc. IUTAM Symposium (Munich, 1977), K. Magnus ed., Springer, Berlin, 1978, pp. 357–376.

    Google Scholar 

  60. Wittenburg, J., Dynamics of Systems of Rigid Bodies, B.G.Teubner, Stuttgart, 1977.

    MATH  Google Scholar 

  61. Wittenburg, J. “Dynamics of multibody systems”, Proc. 15th lut. Congr. of Theoretical and Applied Mechanics, IUTAM/ICTAM (Toronto, 1980), F.P.J. Rimrott, B. Tabarrok eds., pp. 197–207.

    Google Scholar 

  62. Wittenburg, J., Wolz, U., “MESA VERDE: a symbolic program for nonlinear articulated-rigid-body dynamics”, Proc 10th ASME Design Engr. Conf. on Mech. Vibration and Noise (Cincinnati, Sep 1985 ).

    Google Scholar 

  63. Graul, S.F., “Mehrkörpersystem-Algorithmus in Vector-Dyadisches Form für beliebig angeordnete elastischen Substrukturen”, Ph.D. dissertation, T.H.Aachen. 1985.

    Google Scholar 

  64. Rosenthal, D.E., Sherman, M.A., “Symbolic multibody equations via Kane’s method”, AIAA paper 83–803, AAS/AIAA Astrodynamics Specialist Cont. Lake Placid NY. 1983.

    Google Scholar 

  65. Lilov, L., Chirikov, V.A., “On the dynamics equations of systems of interconnected bodies”, PMM 45 (1981), 383–390.

    MATH  Google Scholar 

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Schwertassek, R., Roberson, R.E. (1986). A Perspective on Computer-Oriented Mutlibody Dynamical Formalisms and their Implementations. In: Bianchi, G., Schiehlen, W. (eds) Dynamics of Multibody Systems. IUTAM Symposium. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-82755-6_22

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  • DOI: https://doi.org/10.1007/978-3-642-82755-6_22

  • Publisher Name: Springer, Berlin, Heidelberg

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