메뉴 건너뛰기




Volumn 463, Issue 2084, 2007, Pages 1955-1982

Linearized dynamics equations for the balance and steer of a bicycle: A benchmark and review

Author keywords

Bicycle; Dynamics; Linear; Motorcycle; Non holonomic; Stability

Indexed keywords


EID: 36349022162     PISSN: 13645021     EISSN: 14712946     Source Type: Journal    
DOI: 10.1098/rspa.2007.1857     Document Type: Review
Times cited : (319)

References (90)
  • 2
    • 24644515415 scopus 로고    scopus 로고
    • Bicycle dynamics and control, adapted bicycles for education and research
    • doi:10.1109/MCS.2005.1499389
    • Åström, K. J., Klein, R. E. & Lennartsson, A. 2005 Bicycle dynamics and control, adapted bicycles for education and research. IEEE Control Syst. Mag. 25, 26-47. (doi:10.1109/MCS.2005.1499389)
    • (2005) IEEE Control Syst. Mag , vol.25 , pp. 26-47
    • Åström, K.J.1    Klein, R.E.2    Lennartsson, A.3
  • 3
    • 36349001832 scopus 로고    scopus 로고
    • Hands-free circular motions of a benchmark bicycle
    • doi:10.1098/rspa.2007.1849
    • Basu-Mandal, P., Chatterjee, A. & Papadopoulos, J. M. 2007 Hands-free circular motions of a benchmark bicycle. Proc. R. Soc. A 463, 1983-2003. (doi:10.1098/rspa.2007.1849)
    • (2007) Proc. R. Soc. A , vol.463 , pp. 1983-2003
    • Basu-Mandal, P.1    Chatterjee, A.2    Papadopoulos, J.M.3
  • 4
    • 84919148243 scopus 로고
    • The complete analogy between the matrix equations and the continuous field equations of structural analysis
    • Bruxelles, Belgium: Presses Académiques Européennes
    • Besseling, J. F. 1964 The complete analogy between the matrix equations and the continuous field equations of structural analysis. In Int. Symp. on Analogue and Digital Techniques Applied to Aeronautics: Proceedings, pp. 223-242. Bruxelles, Belgium: Presses Académiques Européennes.
    • (1964) Int. Symp. on Analogue and Digital Techniques Applied to Aeronautics: Proceedings , pp. 223-242
    • Besseling, J.F.1
  • 6
    • 85020822461 scopus 로고    scopus 로고
    • Bourlet, C. 1899 Étude théorique sur la bicyclette. Bull. Soc. Math. France 27, 47-67, 76-96. (Submitted in 1897 for the Prix Fourneyron, awarded first place in 1898.)
    • Bourlet, C. 1899 Étude théorique sur la bicyclette. Bull. Soc. Math. France 27, 47-67, 76-96. (Submitted in 1897 for the Prix Fourneyron, awarded first place in 1898.)
  • 7
    • 36349005949 scopus 로고
    • Aperçu sur la théorie de la bicyclette
    • Boussinesq, J. 1899a Aperçu sur la théorie de la bicyclette. J. Math. Pure Appl. 5, 117-135.
    • (1899) J. Math. Pure Appl , vol.5 , pp. 117-135
    • Boussinesq, J.1
  • 8
    • 36349013831 scopus 로고
    • Complément à une étude récente concernant la théorie de la bicyclette: Influence, sur l'équilibre, des mouvements latéraux spontanés du cavalier
    • Boussinesq, J. 1899b Complément à une étude récente concernant la théorie de la bicyclette: influence, sur l'équilibre, des mouvements latéraux spontanés du cavalier. J. Math. Pure Appl. 5, 217-232.
    • (1899) J. Math. Pure Appl , vol.5 , pp. 217-232
    • Boussinesq, J.1
  • 9
    • 36348967814 scopus 로고
    • Steering and stability of single-track vehicles
    • Bower, G. S. 1915 Steering and stability of single-track vehicles. Automob. Eng. 5, 280-283.
    • (1915) Automob. Eng , vol.5 , pp. 280-283
    • Bower, G.S.1
  • 10
    • 85020837859 scopus 로고    scopus 로고
    • Carvallo, E. 1899 Théorie du mouvement du monocycle et de la bicyclette. Paris, France: Gauthier-Villars. (Submitted in 1897 for the Prix Fourneyron, awarded shared second place in 1898.)
    • Carvallo, E. 1899 Théorie du mouvement du monocycle et de la bicyclette. Paris, France: Gauthier-Villars. (Submitted in 1897 for the Prix Fourneyron, awarded shared second place in 1898.)
  • 12
    • 0039392305 scopus 로고    scopus 로고
    • Angular momentum and motorcycle counter-steering: A discussion and demonstration
    • doi:10.1119/1.19032
    • Cox, A. J. 1998 Angular momentum and motorcycle counter-steering: a discussion and demonstration. Am. J. Phys. 66, 1018-1020. (doi:10.1119/1.19032)
    • (1998) Am. J. Phys , vol.66 , pp. 1018-1020
    • Cox, A.J.1
  • 13
    • 85020784633 scopus 로고    scopus 로고
    • Den Hartog, J. P. 1948 Mechanics. New York, NY; London, UK: McGraw-Hill. (Article 61.)
    • Den Hartog, J. P. 1948 Mechanics. New York, NY; London, UK: McGraw-Hill. (Article 61.)
  • 14
    • 84967948817 scopus 로고
    • Effect of inclination of steering axis and of stagger of the front wheel on stability of motion of a bicycle
    • Dikarev, E. D., Dikareva, S. B. & Fufaev, N. A. 1981 Effect of inclination of steering axis and of stagger of the front wheel on stability of motion of a bicycle. Izv. Akad. Nauk SSSR Mekh. Tverd. Tela 16, 69-73.
    • (1981) Izv. Akad. Nauk SSSR Mekh. Tverd. Tela , vol.16 , pp. 69-73
    • Dikarev, E.D.1    Dikareva, S.B.2    Fufaev, N.A.3
  • 15
    • 85020759598 scopus 로고    scopus 로고
    • Transl
    • [Transl. Mech. Solids 16, 60-63.]
    • Solids , vol.16 , pp. 60-63
    • Mech1
  • 17
    • 36348955113 scopus 로고
    • Die Stabilität von Einspurfahrzeugen
    • doi:10.1007/BF02592590
    • Döhring, E. 1955 Die Stabilität von Einspurfahrzeugen. Forschung Ing. Wes. A 21, 50-62. (doi:10.1007/BF02592590)
    • (1955) Forschung Ing. Wes. A , vol.21 , pp. 50-62
    • Döhring, E.1
  • 19
    • 0034411928 scopus 로고    scopus 로고
    • Steering in bicycles and motorcycles
    • doi:10.1119/1.19504
    • Fajans, J. 2000 Steering in bicycles and motorcycles. Am. J. Phys. 68, 654-659. (doi:10.1119/1.19504)
    • (2000) Am. J. Phys , vol.68 , pp. 654-659
    • Fajans, J.1
  • 20
    • 24644438540 scopus 로고
    • An advanced model of bicycle dynamics
    • doi:10.1088/0143- 0807/11/2/010
    • Franke, G., Suhr, W. & Rieß, F. 1990 An advanced model of bicycle dynamics. Eur. J. Phys. 11, 116-121. (doi:10.1088/0143- 0807/11/2/010)
    • (1990) Eur. J. Phys , vol.11 , pp. 116-121
    • Franke, G.1    Suhr, W.2    Rieß, F.3
  • 21
  • 23
    • 85020800624 scopus 로고
    • Paris, France: Presses Universitaires de France
    • Haag, J. 1955 Les mouvements vibratoire, vol. 2. Paris, France: Presses Universitaires de France.
    • (1955) Les mouvements vibratoire , vol.2
    • Haag, J.1
  • 24
    • 0040744471 scopus 로고
    • Wadsworth, Belmont, CA
    • (Transl. Oscillatory motions, vol. 2, Wadsworth, Belmont, CA, 1962.)
    • (1962) Oscillatory motions , vol.2
  • 26
    • 85020762520 scopus 로고    scopus 로고
    • Herfkens, B. D. 1949 De stabiliteit van het rijwiel. Report S-98-247-50-10-'49, Instituut voor rijwielontwikkeling, 's-Gravenhage.
    • Herfkens, B. D. 1949 De stabiliteit van het rijwiel. Report S-98-247-50-10-'49, Instituut voor rijwielontwikkeling, 's-Gravenhage.
  • 27
  • 28
    • 33744674975 scopus 로고
    • The motorcycle as a gyroscope
    • doi:10.1119/1.1987814
    • Higbie, J. 1974 The motorcycle as a gyroscope. Am. J. Phys. 42, 701-702. (doi:10.1119/1.1987814)
    • (1974) Am. J. Phys , vol.42 , pp. 701-702
    • Higbie, J.1
  • 29
    • 0018737105 scopus 로고
    • Lateral dynamics and stability of the skateboard
    • Hubbard, M. 1979 Lateral dynamics and stability of the skateboard. Trans. ASME J. Appl. Mech. 46, 931-936.
    • (1979) Trans. ASME J. Appl. Mech , vol.46 , pp. 931-936
    • Hubbard, M.1
  • 30
    • 36348997229 scopus 로고
    • Physics and bicycles
    • doi:10.1119/1.1990413
    • Jones, A. T. 1942 Physics and bicycles. Am. J. Phys. 10, 332-333. (doi:10.1119/1.1990413)
    • (1942) Am. J. Phys , vol.10 , pp. 332-333
    • Jones, A.T.1
  • 31
    • 0008957088 scopus 로고
    • The stability of the bicycle
    • Jones, D. E. H. 1970 The stability of the bicycle. Phys. Today 23, 34-40.
    • (1970) Phys. Today , vol.23 , pp. 34-40
    • Jones, D.E.H.1
  • 33
    • 0002592877 scopus 로고
    • SPACAR - computer program for dynamic analysis of flexible spatial mechanisms and manipulators
    • ed. W. Schiehlen, pp, Berlin, Germany: Springer
    • Jonker, J. B. & Meijaard, J. P. 1990 SPACAR - computer program for dynamic analysis of flexible spatial mechanisms and manipulators. In Multibody systems handbook (ed. W. Schiehlen), pp. 123-143. Berlin, Germany: Springer.
    • (1990) Multibody systems handbook , pp. 123-143
    • Jonker, J.B.1    Meijaard, J.P.2
  • 34
    • 0004193247 scopus 로고
    • New York, NY: Holt, Rinehart and Winston
    • Kane, T. R. 1968 Dynamics. New York, NY: Holt, Rinehart and Winston.
    • (1968) Dynamics
    • Kane, T.R.1
  • 35
    • 2442600888 scopus 로고
    • Some nonexplanations of bicycle stability
    • doi:10.1119/1.12246
    • Kirshner, D. 1980 Some nonexplanations of bicycle stability. Am. J. Phys. 48, 36-38. (doi:10.1119/1.12246)
    • (1980) Am. J. Phys , vol.48 , pp. 36-38
    • Kirshner, D.1
  • 36
    • 85020775596 scopus 로고    scopus 로고
    • Klein, F. & Sommerfeld, A. 1910 Über die Theorie des Kreisels. Leipzig, Germany: Teubner. (ch. IX, §8, pp. 863-884.)
    • Klein, F. & Sommerfeld, A. 1910 Über die Theorie des Kreisels. Leipzig, Germany: Teubner. (ch. IX, §8, pp. 863-884.)
  • 38
    • 85020817312 scopus 로고    scopus 로고
    • Kondo, M., Nagaoka, A. & Yoshimura, F. 1963 Theoretical study on the running stability of the two-wheelers. Trans. Soc. Automot. Eng. Jpn 17, 8-18.
    • Kondo, M., Nagaoka, A. & Yoshimura, F. 1963 Theoretical study on the running stability of the two-wheelers. Trans. Soc. Automot. Eng. Jpn 17, 8-18.
  • 40
    • 85020800227 scopus 로고
    • Improvement in velocipedes
    • U.S. Patent 59915
    • Lallement, P. 1866 Improvement in velocipedes. U.S. Patent 59915.
    • (1866)
    • Lallement, P.1
  • 41
    • 24644463617 scopus 로고
    • Dynamical stability of the bicycle
    • doi:10.1088/0143-0807/8/3/013
    • Le Hénaff, Y. 1987 Dynamical stability of the bicycle. Eur. J. Phys. 8, 207-210. (doi:10.1088/0143-0807/8/3/013)
    • (1987) Eur. J. Phys , vol.8 , pp. 207-210
    • Le Hénaff, Y.1
  • 42
  • 43
    • 33749376501 scopus 로고    scopus 로고
    • Bicycles, motorcycles, and models
    • doi:10.1109/MCS.2006. 1700044
    • Limebeer, D. J. N. & Sharp, R. S. 2006 Bicycles, motorcycles, and models. IEEE Control Syst. Mag. 26, 34-61. (doi:10.1109/MCS.2006. 1700044)
    • (2006) IEEE Control Syst. Mag , vol.26 , pp. 34-61
    • Limebeer, D.J.N.1    Sharp, R.S.2
  • 44
    • 36349026569 scopus 로고
    • Controlled and programmed motion of a bicycle on a plane
    • Lobas, L. G. 1978 Controlled and programmed motion of a bicycle on a plane. Izv. Akad. Nauk SSSR Mekh. Tverd. Tela 13, 22-28.
    • (1978) Izv. Akad. Nauk SSSR Mekh. Tverd. Tela , vol.13 , pp. 22-28
    • Lobas, L.G.1
  • 45
    • 85020795387 scopus 로고    scopus 로고
    • [Transl. Mech. Solids 13, 18-24; author's name misspelled into Gobas.]
    • [Transl. Mech. Solids 13, 18-24; author's name misspelled into Gobas.]
  • 47
    • 0008961059 scopus 로고
    • The stability of bicycles
    • doi:10.1119/1.12893
    • Lowell, J. & McKell, H. D. 1982 The stability of bicycles. Am. J. Phys. 50, 1106-1112. (doi:10.1119/1.12893)
    • (1982) Am. J. Phys , vol.50 , pp. 1106-1112
    • Lowell, J.1    McKell, H.D.2
  • 48
    • 85020780036 scopus 로고    scopus 로고
    • Manning, J. R. 1951 The dynamical stability of bicycles. Report RN/1605/JRM, Department of Scientific and Industrial Research, Road Research Laboratory, Crowthorne, Berkshire, UK.
    • Manning, J. R. 1951 The dynamical stability of bicycles. Report RN/1605/JRM, Department of Scientific and Industrial Research, Road Research Laboratory, Crowthorne, Berkshire, UK.
  • 49
    • 85020790633 scopus 로고
    • Why does a bicycle keep upright?
    • doi:10.2307/3611217
    • Maunsell, F. G. 1946 Why does a bicycle keep upright? Math. Gaz. 30, 195-199. (doi:10.2307/3611217)
    • (1946) Math. Gaz , vol.30 , pp. 195-199
    • Maunsell, F.G.1
  • 51
    • 0026404433 scopus 로고
    • Direct determination of periodic solutions of the dynamical equations of flexible mechanisms and manipulators
    • doi:10.1002/nme.1620320811
    • Meijaard, J. P. 1991 Direct determination of periodic solutions of the dynamical equations of flexible mechanisms and manipulators. Int. J. Numer. Methods Eng. 32, 1691-1710. (doi:10.1002/nme.1620320811)
    • (1991) Int. J. Numer. Methods Eng , vol.32 , pp. 1691-1710
    • Meijaard, J.P.1
  • 52
    • 36348980568 scopus 로고    scopus 로고
    • Derivation of the linearized equations for an uncontrolled bicycle
    • Internal report, University of Nottingham, UK
    • Meijaard, J. P. 2004 Derivation of the linearized equations for an uncontrolled bicycle. Internal report, University of Nottingham, UK.
    • (2004)
    • Meijaard, J.P.1
  • 53
    • 85020796008 scopus 로고    scopus 로고
    • Neǐmark, J. I. & Fufaev, N. A. 1972 Dynamics of nonholonomic systems. Providence, RI: American Mathematical Society. (Transl. from the Russian edition, Nauka, Moscow, 1967.)
    • Neǐmark, J. I. & Fufaev, N. A. 1972 Dynamics of nonholonomic systems. Providence, RI: American Mathematical Society. (Transl. from the Russian edition, Nauka, Moscow, 1967.)
  • 54
    • 36348987812 scopus 로고
    • Bicycle dynamics - the meaning behind the math
    • Olsen, J. & Papadopoulos, J. M. 1988 Bicycle dynamics - the meaning behind the math. Bike Tech. 7, 13-15.
    • (1988) Bike Tech , vol.7 , pp. 13-15
    • Olsen, J.1    Papadopoulos, J.M.2
  • 55
    • 85020841445 scopus 로고    scopus 로고
    • Papadopoulos, J. M. 1987 Bicycle steering dynamics and self-stability: a summary report on work in progress. Technical report, Cornell Bicycle Research Project, Cornell University, Ithaca, NY. (Availabe at Ruina's www site).
    • Papadopoulos, J. M. 1987 Bicycle steering dynamics and self-stability: a summary report on work in progress. Technical report, Cornell Bicycle Research Project, Cornell University, Ithaca, NY. (Availabe at Ruina's www site).
  • 57
  • 59
    • 85020816186 scopus 로고    scopus 로고
    • Rankine, W. J. M. 1869 On the dynamical principles of the motion of velocipedes. Engineer 28, pp. 79, 129, 153, 175, 29 (1870), 2.
    • Rankine, W. J. M. 1869 On the dynamical principles of the motion of velocipedes. Engineer 28, pp. 79, 129, 153, 175, 29 (1870), 2.
  • 60
    • 85020819003 scopus 로고
    • Bicycle dynamics, simplified steady state response characteristics and stability indices
    • Report ZN-5431-V-1, June, Calspan, Buffalo, NY
    • Rice, R. S. 1974 Bicycle dynamics, simplified steady state response characteristics and stability indices. Report ZN-5431-V-1, June, Calspan, Buffalo, NY.
    • (1974)
    • Rice, R.S.1
  • 61
    • 85020761040 scopus 로고
    • Bicycle dynamics - simplified dynamic stability analysis
    • Report ZN-5921-V-2, September, Calspan, Buffalo, NY
    • Rice, R. S. 1976 Bicycle dynamics - simplified dynamic stability analysis. Report ZN-5921-V-2, September, Calspan, Buffalo, NY.
    • (1976)
    • Rice, R.S.1
  • 62
    • 0343710021 scopus 로고
    • An evaluation of the performance and handling qualities of bicycles
    • Report VJ-2888-K, April, Calspan, Buffalo, NY
    • Rice, R. S. & Roland, R. D. 1970 An evaluation of the performance and handling qualities of bicycles. Report VJ-2888-K, April, Calspan, Buffalo, NY.
    • (1970)
    • Rice, R.S.1    Roland, R.D.2
  • 63
    • 85020765482 scopus 로고    scopus 로고
    • Roland, R. D. 1973 Computer simulation of bicycle dynamics. In Mechanics and sport (AMD-4, ed. J. L. Bleustein), pp. 35-83. New York, NY: American Society of Mechanical Engineers.
    • Roland, R. D. 1973 Computer simulation of bicycle dynamics. In Mechanics and sport (AMD-4, ed. J. L. Bleustein), pp. 35-83. New York, NY: American Society of Mechanical Engineers.
  • 64
    • 36348935173 scopus 로고
    • Bicycle dynamics tire characteristics and rider modeling
    • Report YA-3063-K-2, March, Calspan, Buffalo, NY
    • Roland, R. D. & Lynch, J. P. 1972 Bicycle dynamics tire characteristics and rider modeling. Report YA-3063-K-2, March, Calspan, Buffalo, NY.
    • (1972)
    • Roland, R.D.1    Lynch, J.P.2
  • 65
    • 36348983414 scopus 로고
    • A digital computer simulation of bicycle dynamics
    • Report YA-3063-K-1, June, Calspan, Buffalo, NY
    • Roland, R. D. & Massing, D. E. 1971 A digital computer simulation of bicycle dynamics. Report YA-3063-K-1, June, Calspan, Buffalo, NY.
    • (1971)
    • Roland, R.D.1    Massing, D.E.2
  • 66
    • 36348967813 scopus 로고
    • On the motion of a bicycle
    • Routh, G. R. R. 1899 On the motion of a bicycle. Messenger Math. 28, 151-169.
    • (1899) Messenger Math , vol.28 , pp. 151-169
    • Routh, G.R.R.1
  • 67
    • 0032133379 scopus 로고    scopus 로고
    • Non-holonomic stability aspects of piecewise holonomic systems
    • doi:10.1016/S0034-4877(98) 80006-2
    • Ruina, A. 1998 Non-holonomic stability aspects of piecewise holonomic systems. Rep. Math. Phys. 42, 91-100. (doi:10.1016/S0034-4877(98) 80006-2)
    • (1998) Rep. Math. Phys , vol.42 , pp. 91-100
    • Ruina, A.1
  • 68
    • 85020824906 scopus 로고    scopus 로고
    • SAE (Society of Automotive Engineers) 2001 Vehicle dynamics terminology - SAE J670e. In 2001 SAE handbook. Warrendale, PA: SAE International.
    • SAE (Society of Automotive Engineers) 2001 Vehicle dynamics terminology - SAE J670e. In 2001 SAE handbook. Warrendale, PA: SAE International.
  • 69
    • 0026255212 scopus 로고
    • Symbolic computer language for multibody systems
    • Sayers, M. W. 1991a Symbolic computer language for multibody systems. J. Guid. Control Dyn. 14, 1153-1163.
    • (1991) J. Guid. Control Dyn , vol.14 , pp. 1153-1163
    • Sayers, M.W.1
  • 70
    • 0026261249 scopus 로고
    • Symbolic vector/dyadic multibody formalism for tree-topology systems
    • Sayers, M. W. 1991b Symbolic vector/dyadic multibody formalism for tree-topology systems. J. Guid. Control Dyn. 14, 1240-1250.
    • (1991) J. Guid. Control Dyn , vol.14 , pp. 1240-1250
    • Sayers, M.W.1
  • 72
    • 0033740702 scopus 로고    scopus 로고
    • Dynamics of flexible multibody systems having rolling contact: Application of the wheel element to the dynamics of road vehicles
    • Schwab, A. L. & Meijaard, J. P. 1999 Dynamics of flexible multibody systems having rolling contact: application of the wheel element to the dynamics of road vehicles. Vehicle Syst. Dyn. Suppl. 33, 338-349.
    • (1999) Vehicle Syst. Dyn. Suppl , vol.33 , pp. 338-349
    • Schwab, A.L.1    Meijaard, J.P.2
  • 73
    • 0043198213 scopus 로고    scopus 로고
    • Dynamics of flexible multibody systems with non-holonomic constraints: A finite element approach
    • doi:10.1023/A:1024575707338
    • Schwab, A. L. & Meijaard, J. P. 2003 Dynamics of flexible multibody systems with non-holonomic constraints: a finite element approach. Multibody Syst. Dyn. 10, 107-123. (doi:10.1023/A:1024575707338)
    • (2003) Multibody Syst. Dyn , vol.10 , pp. 107-123
    • Schwab, A.L.1    Meijaard, J.P.2
  • 74
    • 17044397301 scopus 로고    scopus 로고
    • Benchmark results on the linearized equations of motion of an uncontrolled bicycle
    • Schwab, A. L., Meijaard, J. P. & Papadopoulos, J. M. 2005 Benchmark results on the linearized equations of motion of an uncontrolled bicycle. KSME J. Mech. Sci. Technol. 19, 292-304.
    • (2005) KSME J. Mech. Sci. Technol , vol.19 , pp. 292-304
    • Schwab, A.L.1    Meijaard, J.P.2    Papadopoulos, J.M.3
  • 75
    • 85020814753 scopus 로고    scopus 로고
    • Sharp, A. 1896 Bicycles and tricycles: an elementary treatise on their design and construction. London, UK: Longmans, Green & Co. (Reissued by MIT Press, 1979.)
    • Sharp, A. 1896 Bicycles and tricycles: an elementary treatise on their design and construction. London, UK: Longmans, Green & Co. (Reissued by MIT Press, 1979.)
  • 76
    • 0000200462 scopus 로고
    • The stability and control of motorcycles
    • Sharp, R. S. 1971 The stability and control of motorcycles. J. Mech. Eng. Sci. 13, 316-329.
    • (1971) J. Mech. Eng. Sci , vol.13 , pp. 316-329
    • Sharp, R.S.1
  • 77
    • 84972971152 scopus 로고
    • The lateral dynamics of motorcycles and bicycles
    • Sharp, R. S. 1985 The lateral dynamics of motorcycles and bicycles. Vehicle Syst. Dyn. 14, 265-283.
    • (1985) Vehicle Syst. Dyn , vol.14 , pp. 265-283
    • Sharp, R.S.1
  • 79
    • 84963217639 scopus 로고
    • SAE paper 710273, Society of Automotive Engineers, New York, NY
    • Singh, D. V. & Goel, V. K. 1971 Stability of Rajdoot scooter. SAE paper 710273, Society of Automotive Engineers, New York, NY.
    • (1971) Stability of Rajdoot scooter
    • Singh, D.V.1    Goel, V.K.2
  • 85
    • 10544249219 scopus 로고
    • A method for the automatic stabilization of an unmanned bicycle
    • thesis, Department of Aeronautics and Astronautics, Stanford University, CA
    • Van Zytveld, P. J. 1975 A method for the automatic stabilization of an unmanned bicycle. Engineer's thesis, Department of Aeronautics and Astronautics, Stanford University, CA.
    • (1975) Engineer's
    • Van Zytveld, P.J.1
  • 86
    • 36349029801 scopus 로고
    • The super-sports motor cycle (with an appendix on steering layout)
    • Wallace, J. 1929 The super-sports motor cycle (with an appendix on steering layout). Proc. Inst. Automob. Eng. 24, 161-231.
    • (1929) Proc. Inst. Automob. Eng , vol.24 , pp. 161-231
    • Wallace, J.1
  • 89
    • 0008948980 scopus 로고
    • The stability of the motion of a bicycle
    • Whipple, F. J. W. 1899 The stability of the motion of a bicycle. Quart. J. Pure Appl. Math. 30, 312-348.
    • (1899) Quart. J. Pure Appl. Math , vol.30 , pp. 312-348
    • Whipple, F.J.W.1
  • 90
    • 85020836244 scopus 로고    scopus 로고
    • Wilson, D. G. 2004 Bicycling science, 3rd edn., with contributions by Jim Papadopoulos. Cambridge, MA: MIT Press.
    • Wilson, D. G. 2004 Bicycling science, 3rd edn., with contributions by Jim Papadopoulos. Cambridge, MA: MIT Press.


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.