Global Utilities

La Trobe University
Department of Mathematics and Statistics

Publications by Professor Geoff Prince

Papers

  1. G. E. Prince, P.G.L. Leach, T.M.Kalotas, C.J. Eliezer and R.M. Santilli, The Lie and Lie-admissible Symmetries of Dynamical Systems, Hadronic J. 3, 390-439, (1979).

  2. G. E. Prince and C.J. Eliezer, Symmetries of the Time-Dependent N-dimensional Oscillator, J. Phys. A: Math.Gen. 13, 815-823, (1980).

  3. G. E. Prince and P.G.L. Leach, The Lie Theory of Extended Groups in Hamilton Mechanics, Hadronic J. 3, 941-961, (1980).

  4. G. E. Prince and C.J. Eliezer, On the symmetries of the Classical Kepler Problem, J. Phys. A: Math. Gen. 14, 587-596, (1981).

  5. G. E. Prince, Toward a Classification of Dynamical Symmetries in Classical Mechanics, Bull. Aust. Math. Soc. 27, 53-71, (1983).

  6. G. E. Prince, Reflections on the symmetry conservation law duality and the Runge-Lenz vector, J. Phys. A: Math.Gen. 16, L105-L108, (1983).

  7. G. E. Prince, Toward a Classification of Dynamical Symmetries in Lagrangian Systems, Proceedings of the IUTAM-ISIMM Symposium on Modern Developments in Analytical Mechanics, June 7-11, 1982 Torino, Italy. Att. D.Accad. d. Sc. d. Torino, Suppl. 117, 687-691 (1983).

  8. G. E. Prince, Homothetic Killing Tensors, Physics Letters A 97A, 133-136, (1983).

  9. G. E. Prince and M. Crampin, Projective differential geometry and geodesic conservation laws in general relativity, I: projective actions, Gen. Rel. Grav. 16, 921-942, (1984).

  10. G. E. Prince and M. Crampin, Projective differential geometry and geodesic conservation laws in general relativity, II: conservation laws, Gen. Rel. Grav. 16, 1063-1075, (1984).

  11. M. Crampin and G. E. Prince, The geodesic spray, the vertical projection, and Raychaudhuri's equation, Gen. Rel. Grav. 16, 675-689, (1984).

  12. M. Crampin, G. E. Prince and G. Thompson, A geometrical version of the Helmholtz conditions in time-dependent Lagrangian dynamics, J. Phys. A: Math.Gen. 17, 1437-1447, (1984).

  13. M. Crampin and G. E. Prince, Equivalent Lagrangian and dynamical symmetries: some comments, Phys. Lett. 108A, 191-194, (1985).

  14. M. Crampin and G. E. Prince, Generalizing gauge freedom for spherically symmetric potentials, J. Phys. A: Math. Gen. 18, 2167-2175, (1985).

  15. G. E. Prince, A complete classification of dynamical symmetries in classical mechanics, Bull. Austral. Math. Soc. 32, 299-308 (1985).

  16. M. Crampin and G. E. Prince, Alternative Lagrangians for spherically symmetric potentials, J. Math. Phys. 29,1551-1555 (1988).

  17. W. Sarlet, G. E. Prince and M. Crampin, Adjoint symmetries for time-dependent second-order equations, J. Phys. A: Math. Gen. 23, 1335-1347, (1990).

  18. S. E. Godfrey and G. E. Prince, A canonical reduction of order for the Kepler problem, J. Phys. A: Math. Gen. 24, 5465-5475, (1991).

  19. J. Sherring and G. E. Prince, Geometric aspects of reduction of order, Trans. Am. Math. Soc. 334, 433-453, (1992).

  20. M. Crampin, W. Sarlet, E. Martinez, G. B. Byrnes and G. E. Prince, Toward a geometrical understanding of Douglas's solution of the inverse problem in the calculus of variations, Inverse Problems 10, 245-260, (1994).

  21. G. E. Prince, G. B. Byrnes, J. Sherring and S. E. Godfrey, A generalization of the Liouville-Arnol'd theorem, Math. Proc. Camb. Phil. Soc. 117, 353-370, (1995).

  22. J. Sherring, A.K. Head and G.E. Prince, DIMSYM and LIE: symmetry determination packages, Mathl. Comput. Modelling 25, 153-164 (1997).

  23. J.E.R. O'Connor and G.E. Prince, Finding Collineations of Kimura Metrics, Gen. Rel. Grav. 30, 69-82, (1998).

  24. J.E. Aldridge and G.E. Prince, Computer Algebra Solution of the Inverse Problem in the Calculus of Variations, Comp. Physics Comm. 115, 489-509, (1998).

  25. M. Jerie, J.E.R. O'Connor and G.E. Prince, Computer Algebra Determination of Symmetries in General Relativity, Comp. Physics Comm. 115 , 363-380, (1998).

  26. G.E. Prince, J.E. Aldridge and G.B. Byrnes, A Universal Hamilton-Jacobi Equation for Second Order ODE's, J. Phys. A: Math. Gen. 32, 827-844, (1999).

  27. M. Jerie, J.E.R. O'Connor and G.E. Prince, Spacetime symmetries for the Kerr metric Class. Quantum Grav. 16, 2885-2887, (1999).

  28. M. Crampin, G.E. Prince, W. Sarlet and G. Thompson, The inverse problem of the calculus of variations: separable systems, Acta Appl. Math. 57, 239-254, (1999).

  29. G. E. Prince, J. Aldridge, S. E. Godfrey and G. B. Byrnes, The Separation of the Hamilton-Jacobi Equation for the Kerr Metric. Proceedings of the First Australian General Relativity Workshop, September 26-30, 1994, Canberra, J. Aust. Math. Soc. B 41, 248-259 (1999).

  30. G.E. Prince, Reply to 'Some remarks on the symmetries of the Kerr spacetime', Class. Quantum Grav. 17, 2027-2028, (2000).

  31. M. Jerie and G.E. Prince, A general Raychaudhuri's equation for second order differential equations, Corrected May 23, 2000. J. Geom. Phys. 34, 227-241, (2000).

  32. G.E. Prince, Quadratic forms associated with planar endomorphisms, Bull. Austral. Math. Soc. 62, 459-465, (2000).

  33. M. Barco and G.E. Prince, Solvable symmetry structures in differential forms applications, Acta Appl. Math. 66, 89-121, (2001).

  34. M. Barco and G.E. Prince, New symmetry solution techniques for first order non-linear PDEs, Appl. Math. Comput. 124, 169-196, (2001).

  35. G. Thompson and G.E. Prince, The inverse problem for flat kinetic minus potential Lagrangians, Extr. Math. 16, 241-248, (2001).

  36. W. Sarlet, G. Thompson and G.E. Prince, The inverse problem of the calculus of variations: the use of geometrical calculus in Douglas's analysis (PDF 231KB), Trans. Am. Math. Soc. 354, 2897-2919 (2002).

  37. M. Jerie and G.E. Prince, Jacobi fields and linear connections for arbitrary second order ODE's (PDF 251KB). J. Geom. Phys. 43, 351-370, (2002).

  38. G.E. Prince and M.Jerie, Generalising Raychaudhuri's equation Proceedings of the 8th International Conference on Differential Geometry and its Applications (PDF 154KB), Opava, 27-31 August 2001, Part II. (Mathematical Publications 3, Silesian University at Opava).

  39. D. Krupka, O. Krupková, G. Prince, and W. Sarlet, Contact symmetries and variational sequences (PDF 182KB). Proc. 9th Internat. Conf. on Diff. Geom. Appl., Prague, 2004, Charles University, Prague, 599-609 (2005).

  40. J. E. Aldridge, G. E. Prince, W. Sarlet and G. Thompson, An EDS approach to the inverse problem in the calculus of variations (PDF 228KB), J. Math. Phys. 47, 103508:1-22 (2006).

  41. D. Krupka, O. Krupková, G.E. Prince and W. Sarlet, Contact Symmetries of the Helmholtz Form (PDF 219KB), Diff. Geom. Appl. 25, 518-542 (2007).

  42. O. Krupková and G. Prince, Lepage forms, closed two-forms and second order ordinary differential equations, Izv. Vyssh. Uchebn. Zaved. Mat. (Russian Mathematics) (N.I.Lobachevskii anniversary volume) 51, 1-16 (2007).

  43. G.E. Prince and S.P. Dubois, Mathematical Models for Motion of the Rear Ends of Vehicles (PDF 264KB), in Mathematical and Computer Modelling 49, 2049-2060 (2009).

  44. G.E. Prince, Comment: "Period function and normalizers of vector fields in Rn with n−1 first integrals" by D. Peralta-Salas, JDE 244, (2008) 1287-1303. J. Diff. Eqns 246, 3750-3753 (2009).

  45. W. Sarlet, G.E. Prince and M. Crampin, Generalized submersiveness of second-order ordinary differential equations. J. Geom. Mech. 1, 209-221 (2009).

Book Chapters

  1. G.E. Prince, The Inverse Problem in the Calculus of Variations and its Ramifications in Geometric Approaches to Differential Equations (PDF 140KB), edited by P. Vassiliou and I. Lisle, Lecture Notes of the Australian Mathematical Society, CUP (March, 2000). (Introductory section only is available on the current page).

  2. G.E.Prince, A Note on the Integrability and Closure Conditions in the Inverse Problem in the Calculus of Variations (PDF 168KB), in Applied Differential Geometry and Mechanics: Volume in Honour of the 60th Birthday of Michael Crampin, edited by W.Sarlet and F.Cantrijn, Gent, Academia Press (2003).

  3. G.E. Prince and D.M. King, The inverse problem in the calculus of variations: nonexistence of Lagrangians (PDF 151KB), pp131-140, in Differential Geometric Methods on Mechanics and Field theory: Volume in Honour of Willy Sarlet, edited by F.Cantrijn and B. Langerock, Gent, Academia Press (2007).

  4. O. Krupková and G. Prince, Second Order Ordinary Differential Equations in Jet Bundles and the Inverse Problem of the Calculus of Variations (PDF 358KB), pp 837-904, in Handbook of Global Analysis, edited by D. Krupka and D. Saunders, Elsevier (2007).

  5. G. E. Prince, On the inverse problem for autoparallels (PDF 157KB), pp 341-351 in "Variations, Geometry and Physics" in honour of Demeter Krupkas sixty-fifth birthday, O. Krupková and D.J. Saunders (Editors) Nova Science Publishers (2009).

Reviews

  1. G.E. Prince, Reduce - a User's View. Math. Scientist, 12, 91-96 (1987).

  2. G.E. Prince, Computer Algebra and Differential equations. Gaz. Aust. Math. Soc., 18, 83-85 (1991).

Submitted

  1. G.E. Prince, G. Stathopoulos and P. Martin, The Geometry of Planar Flows (PDF 915KB).


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