Vrije Universiteit Brussel

Publications

  1. R. VAN DOOREN, Invloed van de randvoorwaarden op de quantisatie van de energie, Publicaties SEMINARIE VAN MECHANICA, TW, VUB-ULB (1968) 45-78.

  2. R. VAN DOOREN, Invloed van de randvoorwaarden op de quantisatie van de energie in de vergelijking van Dirac, KONINKLIJKE VLAAMSE ACADEMIE VAN BELGIE, KLASSE DER WETENSCHAPPEN 30 (1968) 1-21.

  3. R. VAN DOOREN, Eindige randvoorwaarden in kwantummechanica, Publicaties DIENST ANALYTISCHE MECHANICA, TW, VUB (1969) 1-61.

  4. P. JANSSENS, M. DELCHAMBRE et R. VAN DOOREN, Sur les oscillateurs non-linéaires du type de Duffing à deux degrés de liberté, INTERNATIONAL CONGRES, Publications CBRM MONS (1969) 171-184.

  5. R. VAN DOOREN, Sur les oscillations composées du type additif d’un système vibraoire non-linéaire amorti à deux degrés de liberté, INTERNATIONAL CONGRES EQUA-DIFF 70 (MARSEILLE 1970) 1-59.

  6. R. VAN DOOREN, Numerical computation of coupled vibrations in forced non-linear undamped two degree of freedom systems, SEMINARIE LABORATORIUM TOEGEPASTE MECHANICA, UNIVERSITEIT BIRMINGHAM (1971) 1-25.

  7. R. VAN DOOREN, Recherche numérique d’oscillations composées du type additif dans un système oscillant non-linéaire amorti à deux degrés de liberté, ACADEMIE ROYALE DE BELGIQUE, CLASSE DES SCIENCES 57 (1971) 524-544.

  8. P. JANSSENS M. DELCHAMBRE et R. VAN DOOREN, L’influence de conditions aux limites à distance finie sur la quantification de l’atome d’hydrogène, ACADEMIE ROYALE DE BELGIQUE, CLASSE DES SCIENCES 57 (1971) 545-558.

  9. R. VAN DOOREN, Harmonische trillingen en somtonen in niet-lineaire mechanische stelsels (1971) (Doctoraatsthesis) 1-314.

  10. R. VAN DOOREN, Combination tones of summed type in a non-linear damped vibratory system with two degrees of freedom, INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS 6 (1971) 237-254.

  11. R. VAN DOOREN, Forced oscillations in coupled Duffing equations by an analytical method of varying amplitudes and phase angles, KONINKLIJKE VLAAMSE ACADEMIE VAN BELGIE, KLASSE DER WETENSCHAPPEN 34 (1972) 1-27.

  12. R. VAN DOOREN, An analytical method for certain weakly non-linear periodic differential systems, ACADEMIE ROYALE DE BELGIQUE, CLASSE DES SCIENCES 58 (1972) 605-621.

  13. R. VAN DOOREN, Etude d’oscillations composées d’un système mécanique non-linéaire à plusieurs degrés de liberté, SEMINARIE CNRS MARSEILLE (1973) 1-27.

  14. R. VAN DOOREN, Recherches de solutions d’équations différentielles fortement non-linéaires, INTERNATIONAL CONGRES EQUA-DIFF 73 (BRUXELLES ET LOUVAIN-LA-NEUVE 1973) Hermann, 324-344.

  15. R. VAN DOOREN, Stabilization of Cowell’s finite difference method for numerical integration of the free Duffing equation, INTERNATIONAL CONGRES POINT MAPPING AND ITS APPLICATIONS (TOULOUSE 1973) CNRS 229, 275-283.

  16. R. VAN DOOREN, Numerical computation of forced oscillations in coupled Duffing equations, NUMERISCHE MATHEMATIK 20 (1973) 300-311.

  17. R. VAN DOOREN, An analytical method for certain highly non-linear periodic differential equations, FUNKCIALAJ EKVACIOJ 16 (1973) 169-180.

  18. R. VAN DOOREN, Differential tones in a damped mechanical system with quadratic and cubic non-linearities, INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS 8 (1973) 575-583.

  19. R. VAN DOOREN, Stabilization of Cowell’s classical finite difference method for numerical integration, JOURNAL OF COMPUTATIONAL PHYSICS 16 (1974) 186-192.

  20. R. VAN DOOREN, Orbit computation in celestial mechanics by Urabe’s method, RESEARCH INSTITUTE FOR MATHEMATICAL SCIENCES 9 (1974) 535-542.

  21. R. VAN DOOREN, Two mode subharmonic vibrations of order 1/9 of a non-linear beam forced by a two mode harmonic load, JOURNAL OF SOUND AND VIBRATION 41 (1975) 133-142.

  22. R. VAN DOOREN, The generalized Hamilton-Jacobi method for non-holonomic dynamical systems of Chetaev’s type, ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK 55 (1975) 407-411.

  23. R. VAN DOOREN, On a new form of the Lagrange equations, JOURNAL OF APPLIED MATHEMATICS AND PHYSICS 26 (1975) 629-632.

  24. R. VAN DOOREN AND R. BOUC, Two mode subharmonic and harmonic vibrations of a non-linear beam forced by a two mode harmonic load, INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS 10 (1975) 271-280.

  25. R. VAN DOOREN, Forced two mode subharmonic vibrations of a nonlinear beam by a new analytical method, 7th INTERNATIONAL CONGRESS ON NONLINEAR OSCILLATIONS (ICNO, BERLIJN, 1975) 1-16.

  26. R. VAN DOOREN, Generalized methods for nonholonomic systems with applications in various fields of classical mechanics, 14th INTERNATIONAL CONGRESS ON THEORETICAL AND APPLIED MECHANICS (IUTAM, DELFT 1976), North-Holland, 373-391.

  27. R. VAN DOOREN, Magnetohydrodynamic pipe flow with variable wall porosity, JOURNAL OF APPLIED MECHANICS 43 , TRANS. ASME 98 (1976) 172-173.

  28. R. VAN DOOREN, Porous pipe flow, THE PHYSICS OF FLUIDS 19 (1976) 481-482.

  29. R. VAN DOOREN, Motion of a rolling disc by a new generalized Hamilton-Jacobi method, JOURNAL OF APPLIED MATHEMATICS AND PHYSICS 27 (1976) 501-505.

  30. R. VAN DOOREN, Forced two mode subharmonic vibrations of a non-linear beam by a new analytical method, ABHANDLUNGEN DER WISSENSCHAFTEN DER DDR 5 (1977) 253-260.

  31. R. VAN DOOREN, Derivation of the Lagrange equations for nonholonomic Chetaev systems from a modified Pontryagin maximum principle, JOURNAL OF APPLIED MATHEMATICS AND PHYSICS 28 (1977) 729-734.

  32. R. VAN DOOREN, Solution of differential equations in Chebyshev series, ACADEMIE ROYALE DE BELGIQUE, CLASSE DES SCIENCES 64 (1978) 360-382.

  33. R. VAN DOOREN, Numerical methods for ordinary differential equations, INTERNATIONAL CONGRES EQUA-DIFF 78 (FLORENCE 1978) 1-24.

  34. R. VAN DOOREN, Solution of integral equations in Chebyshev series, COLLOQIUM LOUVAIN-LA-NEUVE (1978) 1-25.

  35. R. VAN DOOREN, Analytical solutions of viscous flow in constricted or widened tubes, JOURNAL OF APPLIED MECHANICS 45 , TRANS. ASME 100 (1978) 241-245.

  36. R. VAN DOOREN, Second form of the generalized Hamilton-Jacobi method for nonholonomic dynamical systems, JOURNAL OF APPLIED MATHEMATICS AND PHYSICS 29 (1978) 828-834.

  37. R. VAN DOOREN, On the generalized Hamilton-Jacobi method for nonholonomic dynamical systems, DIENST ANALYTISCHE MECHANICA, TW, VUB (1979) 1-6.

  38. R. VAN DOOREN, Stability of solitary waves in shallow water, THE PHYSICS OF FLUIDS 22 (1979) 1586-1588.

  39. R. VAN DOOREN, Generalized methods for nonholonomic systems with applications in various fields of classical mechanics, MIR (1979) 598-624 (Russische vertaling).

  40. H. JANSSEN, J. VLASSENBROECK and R. VAN DOOREN, Integration method for systems of differential equations based on Chebyshev polynomials, INTERNATIONAL CONGRESS ZURICH (1980) 1-24.

  41. R. VAN DOOREN and J. VLASSENBROECK, A new look at the brachystochrone problem, JOURNAL OF APPLIED MATHEMATICS AND PHYSICS 31 (1980) 785-790.

  42. J. SCHOUKENS, R. VAN DOOREN et al., Bepalen van de parameters van een transferfunktie met behulp van ortogonale funkties, DIENST ELEKTRICITEIT (1981) 1-3.

  43. R. VAN DOOREN and J. VLASSENBROECK, A computational method in optimal systems control with various applications, 3rd IMA CONGRESS ON CONTROL THEORY (SHEFFIELD), Academic Press (1981) 407-429.

  44. R. VAN DOOREN, Computational aspects of non-linear oscillations, EUROMECH COLLOQIUM 141 (ENSCHEDE 1981) 1-45.

  45. J. VLASSENBROECK, H. JANSSEN and R. VAN DOOREN, A direct Chebyshev approach with practical applicability on optimal control problems, 8th WORLD CONGRESS IFAC (KYOTO 1981), Pergamon, 159-164.

  46. J. VLASSENBROECK and R. VAN DOOREN, Estimation and measurement of the mechanical parameters of the respiratory system, INTERNATIONAL CONGRESS BRIGHTON (1982) 1-27.

  47. J. SCHOUKENS, R. VAN DOOREN et al., Technological and methodological advances in measurement, ACTA IMEKO (1982).

  48. R. VAN DOOREN and J. VLASSENBROECK, Chebyshev series solution of the controlled Duffing oscillator, JOURNAL OF COMPUTATIONAL PHYSICS 47 (1982) 321-329.

  49. R. VAN DOOREN, Numerical computation of solutions to the KdV equation in double Chebyshev series, JOURNAL OF APPLIED MATHEMATICS AND PHYSICS 34 (1983) 118-123.

  50. J. VLASSENBROECK and R. VAN DOOREN, Estimation of the mechanical parameters of the human respiratory system, MATHEMATICAL BIOSCIENCES 69 (1984) 31-55.

  51. R. VAN DOOREN, The three-soliton solution of the two-dimensional Korteweg-de-Vries equation, ADVANCES IN NONLINEAR WAVES 111 (1985) 187-198.

  52. R. VAN DOOREN, A direct method for obtaining N-soliton solutions of nonlinear wave equations, DIENST ANALYTISCHE MECHANICA, TW, VUB (1986) 1-8.

  53. R. VAN DOOREN, On chaotic behaviour in the Duffing oscillator, 7th INTERNATIONAL COLLOQIUM DYNAMICS DAYS (TWENTE 1986) 1-28.

  54. R. VAN DOOREN and H. JANSSEN, Period doubling bifurcations in the Duffing oscillator, 8th INTERNATIONAL COLLOQIUM DYNAMICS DAYS (DUSSELDORF 1987) 1-20.

  55. H. JANSSEN and R. VAN DOOREN, Numerical study of harmonics and subharmonics of the Duffing oscillator in the neighborhood of a strange attractor, 8th INTERNATIONAL COLLOQIUM DYNAMICS DAYS (DUSSELDORF 1987) 21-33.

  56. R. VAN DOOREN, Numerical study of the controlled Van der Pol oscillator in Chebyshev series, JOURNAL OF APPLIED MATHEMATICS AND PHYSICS 38 (1987) 934-939.

  57. H. JANSSEN and R. VAN DOOREN, Numerical study of certain attractors by a Gauss-Legendre integration method, 3rd INTERNATIONAL CONGRESS ON COMPUTATIONAL AND APPLIED MATHEMATICS (ICCAM, LEUVEN, 1988) 1-20.

  58. J. VLASSENBROECK and R. VAN DOOREN, A Chebyshev technique for solving nonlinear optimal control problems, IEEE TRANSACTIONS ON AUTOMATIC CONTROL 33 (1988) 333-340.

  59. R. VAN DOOREN, On the transition from regular to chaotic behaviour in the Duffing oscillator, JOURNAL OF SOUND AND VIBRATION 123 (1988) 327-339.

  60. R. VAN DOOREN and H. JANSSEN, Period doubling solutions in the Duffing oscillator: a Galerkin approach, JOURNAL OF COMPUTATIONAL PHYSICS 81 (1989) 161-171.

  61. R. VAN DOOREN, A Chebyshev technique applied to a controlled nuclear reactor system, OPTIMAL CONTROL APPLICATIONS AND METHODS 10 (1989) 285-291.

  62. H. JANSSEN and R. VAN DOOREN, A one-step integration routine for normal differential systems based on Gauss-Legendre quadrature, JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 28 (1989) 207-217.

  63. R. VAN DOOREN, Period doubling bifurcations in a laser model, DIENST ANALYTISCHE MECHANICA, TW, VUB (1991) 1-10.

  64. R. VAN DOOREN, Rigorous studies of a Duffing oscillator, JOURNAL OF SOUND AND VIBRATION 155 (1992) 368-369.

  65. R. VAN DOOREN, M. DE GROOTE and H. JANSSEN, Numerical evidence of Feigenbaum’s number d in non-linear oscillations, JOURNAL OF COMPUTATIONAL PHYSICS 105 (1993) 173-177.

  66. R. VAN DOOREN and H. JANSSEN, A new period doubling Feigenbaum sequence for a Duffing system with large forcing, GENERAL SCIENTIFIC MEETING, UITGAVE K.U. LEUVEN (1993) 58.

  67. R. VAN DOOREN and H. JANSSEN, A new Feigenbaum sequence of period doubling bifurcations for a periodic excited buckled beam, ACTES DU 11ème CONGRES FRANCAIS DE MECANIQUE (LILLE-VILLENEUVE D’ASCQ) Vol. 5 (1993) 101-104.

  68. R. VAN DOOREN, Reguliere en chaotische bewegingen in niet-lineaire dynamische systemen, SEMINARIE DIENST WERKTUIGKUNDE, TW, VUB (1994) 1-49.

  69. R. VAN DOOREN, In: Professor R.E. JONCHEERE, Publicaties DIENST WERKTUIGKUNDE, TW, VUB (1994) 197-209 (reprint).

  70. R. VAN DOOREN, Bifurcations in a pendulum with circular support motion, NFWO COLLOQIUM ULB (1994) 1-27.

  71. R. VAN DOOREN and H. JANSSEN, Period doubling bifurcations in a parametrically excited Duffing oscillator, PROCEEDINGS 3rd CONGRESS ON THEORETICAL AND APPLIED MECHANICS (LIEGE 1994) 173-176.

  72. R. VAN DOOREN and H. JANSSEN, A continuation algorithm for discovering new chaotic motions in forced Duffing systems, 6th INTERNATIONAL CONGRESS ON COMPUTATIONAL AND APPLIED MATHEMATICS (ICCAM, LEUVEN, 1994) 1-25.

  73. H. JANSSEN and R. VAN DOOREN, Application of high-order difference methods for the study of period doubling bifurcations in nonlinear oscillators, 6th INTERNATIONAL CONGRESS ON COMPUTATIONAL AND APPLIED MATHEMATICS (ICCAM, LEUVEN, 1994) 1-31.

  74. R. VAN DOOREN, Regular and chaotic motions in a two-link planar robot system with applied periodic torque, DIENST WERKTUIGKUNDE, TW, VUB (1995) 1-36.

  75. R. VAN DOOREN, Bifurcations et chaos dans un modèle dynamique d’un robot, ACTES DU 12eme CONGRES FRANCAIS DE MECANIQUE (STRASBOURG) PUBLICATIONS A.U.M., VOL. 4 (1995) 53-56.

  76. R. VAN DOOREN and H. JANSSEN, A continuation algorithm for discovering new chaotic motions in forced Duffing’s systems, JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 66 (1996) 527-541.

  77. H. JANSSEN and R. VAN DOOREN, Applications of high order difference methods for the study of period doubling bifurcations in nonlinear oscillators, JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 66 (1996) 293-313.

  78. R. VAN DOOREN, Chaos in a pendulum with forced horizontal support motion, CHAOS, SOLITONS AND FRACTALS 7 (1996) 77-90.

  79. R. VAN DOOREN, Bifurcations and chaos in a pendulum with circular support motion, INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS 6 (1996) 745-749.

  80. R. VAN DOOREN, Zones of chaotic behaviour in the parametrically excited pendulum, JOURNAL OF SOUND AND VIBRATION 200 (1997) 105-109.

  81. R. VAN DOOREN, New features on bifurcations and chaos in coupled forced Duffing oscillators, PROCEEDINGS OF THE 4th CONGRESS ON THEORE-TICAL AND APPLIED MECHANICS (LEUVEN 1997) 39-42.

  82. R. VAN DOOREN, Harmonic balance and continuation techniques in the dynamic analysis of Duffing’s equation, JOURNAL OF SOUND AND VIBRATION 221 (1999) 525-529.

  83. R. VAN DOOREN, A frequency domain based numeric-analytical method for non-linear dynamical systems, JOURNAL OF SOUND AND VIBRATION 226 (1999) 799-804.

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