Rigid Body Kinematics

Algebraic and geometric methods in rigid body kinematics and dynamics

  • By using the Lie group structure of the rigid rotations, and the associated Lie algebra, the tensor calculus is used as a tool in the study of the vector fields associated to the velocities and accelerations (up the the nth order) of the rigid body.
  • A new set of procedures is developed in order to analytically determine the velocities and accelerations disctribution in a rigid body only from a minimal set of direct measurements. This procedure is developped in a coordinate-free form, and it allows the establishment of precise computation algorithms.
  • A symbolic procedure to model the motion with respect to a non-inertial reference frame is developed. It is proven that it exists a bilateral smooth transfer between the aforementioned motion and the motion with respect to an inertial reference frame. This transfer is modeled by a proper orthogonal tensor valued function of real variable, which is determined analytically.
  • This symbolic procedure, which is mostly associated with rigid body methods, also allows to offer new vectorial coordinate-free closed form solutions to some classical single-particle problems:
    • The Foucault Pendulum problem
    • The Kepler problem in a rotating reference frame
    • The relative motion in a central force field, which leads to the closed form solution to the relative motion in a Newtonian potential field (the reader is refered here for a more detailed presentation of this result)
    • The reduction of the motion in a central force field to a Keplerian motion

References:

  1. Condurache D., A New General investigation of the Kinematics of the Rigid Bodies, ISBN 973-9476-21-X, Polirom, 2000.
  2. Condurache D., Reprezentari simbolice. Aplicatii in teoria semnalelor si studiul sistemelor dinamice, ISBN 973-97101-8-2, Nord-Est, Iasi, 1996, 218 pag.
  3. Condurache, D., Matcovschi M. H., Fundamentele matematice ale mecanicii robotilor, www.ac.tuiasi.ro/ro/library/Fdm_Mec_Rob/index.html, 2000.
  4. Condurache, D., Martinusi, V., Foucault Pendulum-like problems: A Tensorial Approach, International Journal of Non-linear Mechanics, vol. 43, issue 8, 2008, pp. 743-760.
  5. Condurache D., Matcovschi M.H, Computation of angular velocity and acceleration tensors by direct measurements ,Acta Mechanica, Vol. 153, No. 3-4, 2002, pp. 147-167.
  6. Condurache D., Matcovschi M.H, Algebraic computation of the twist of a rigid body through direct measurements, Comput.Methods Appl.Mech.Engrg.Vol. 190, No. 40-41, 2001, pp. 5357-5376.
  7. Condurache D., The Lagrangian in a Nonstationary Electromagnetic Field in Non-Inertial Frames, Bul. Inst. Polit. Iasi, XLVII (LI),1-2,s.I., 2001, pp.87-96.
  8. Condurache D., Matcovschi M.H., Explicit Solution to Some Vectorial Differential Equation. II. Applications to Theoretical Mechanics, Bul. Inst. Polit. Iasi, XLVII (LI),1-2, s.I., 2001, pp. 315-325.
  9. Condurache D., Matcovschi M.H., Explicit Solution to Some Vectorial Differential Equations. I. General Results, Bul. Inst. Polit. Iasi, XLVII (LI),1-2, s.I,. 2001, pp. 303-313.
  10. Condurache D., A General Method to Obtain an Exact Vectorial Solution to Foucault`s Pendulum Problem , Bul. Inst. Iasi, XLVI(L), 1-2, sI, 2000, pp. 79-96.
  11. Condurache D., Remark on the movement in an elastic field, Bul. Inst. Polit. Iasi, XlV (XLIX),3-4, s.I, 1999, pp.85-94.
  12. Condurache D., On the composition of three spatial harmonic oscillations, Bul. Inst. Polit. Iasi, XLV (XLIX), 1-2,s.I, 1999, pp. 87-94.
  13. Condurache D., On the motion of a charged particle in a non-stationary electric and magnetic field, Bul. Inst. Iasi, XLV (XLIX),1-2,s.III, 1999, pp. 7-16.
  14. Condurache D., New Generalization of Poisson Formulae, Bul. Inst. Polit. Iasi, XLIV (XLVIII),3-4, s.I, 1998, pp 75-89.
  15. Condurache D., On the Acceleration Field of a Rigid Body under General  Motion, Bul. Inst. Polit. Iasi, XLIV (XLVIII),1-2,s.I.,1998, pp. 67-73.
  16. Condurache D., An Exact Solution to Foucault`s Pendulum Problem, Bul. Inst. Polit. Iasi, XLIII (XLVII), 3-4,s.I, 1997, pp. 83-92.
  17. Condurache D., Braier A., A Method for the Direct Integration in the Study of Problems of Theoretical Mechanics, Bul. Inst. Polit. Iasi, XLI (XLV),1-2,s.I., 1995, pp. 14-25.
  18. Braier A., Condurache D., On the Instantaneous Angular Velocity Vector, Bul. Inst. Polit. Iasi, XXX (XXXIV), 1-4, sIII, 1984, pp. 25-58.
  19. Condurache, D., Martinuşi, V., Computing the Field of nth Order Accelerations in Rigid Motion by Direct Measurements, “The 2nd International Conference “Advanced Concepts in Mechanical Engineering””, Iasi , 15-17 iun., 2006.
  20. Condurache, D., Martinuşi, V., A Tensorial Explicit Solution to Darboux Equation, “The 2nd International Conference <<Advanced Concepts in Mechanical Engineering>>”, Iasi ,15-17 iun., 2006.
  21. Condurache, D., Martinuşi, V., Computing the Logarithm of Homogenous Matrices in SE(3), 1st International Conference ²Computational Mechanics and Virtual Engineering ² COMEC 2005, Braşov, 2005.
  22. Condurache D., Matcovschi M.H., On the n-Order Acceleration Distribution during Rigid Motion, 7-th International Symposium on Automatic Control and Computer Science, Iasi, Romania, 2001.
  23. Condurache D., Un procedeu simbolic in studiul dinamicii relative a particulei materiale, in volumul «Conceptie, tehnologie si management in constructia de masini», Institutul Politehnic «Gh. Asachi» Iasi, 1992.
  24. Condurache D., Asupra solutiilor matriciale ale unor ecuatii diferentiale vectoriale, Sesiunea stiintifica «Creatia tehnica si fiabilitatea in constructia de masini», Iasi, 1985.

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