메뉴 건너뛰기




Volumn 17, Issue , 2010, Pages 45-86

Euler's elastica and beyond

Author keywords

[No Author keywords available]

Indexed keywords


EID: 77954396309     PISSN: 13125192     EISSN: 13145673     Source Type: Journal    
DOI: 10.7546/jgsp-17-2010-45-86     Document Type: Article
Times cited : (42)

References (83)
  • 1
    • 0012737190 scopus 로고    scopus 로고
    • Willmore-chern tubes on tomogeneous spaces in warped product spaces
    • Arroyo J., Barros M. and Garay O., Willmore-chern tubes on tomogeneous spaces in warped product spaces, Pacific. J. Math. 188 (1999) 201-207.
    • (1999) Pacific. J. Math. , vol.188 , pp. 201-207
    • Arroyo, J.1    Barros, M.2    Garay, O.3
  • 2
    • 0004178623 scopus 로고
    • Penguin Books Ltd., New York, 1937, translated to Japanese by Y. Tanaka and H. Ginbayashi, Tokyo-tosho, Tokyo
    • Bell E., Men of Mathematics, Penguin Books Ltd., New York, 1937, (translated to Japanese by Y. Tanaka and H. Ginbayashi, Tokyo-tosho, Tokyo 1976).
    • (1976) Men of Mathematics
    • Bell, E.1
  • 4
    • 0001124224 scopus 로고
    • On the hyperelliptic sigma functions
    • Baker H., On the hyperelliptic sigma functions, Am. J. Math. 20(1898) 301-384.
    • (1898) Am. J. Math. , vol.20 , pp. 301-384
    • Baker, H.1
  • 5
    • 0000252859 scopus 로고
    • On a system of differential equations leading to periodic functions
    • Baker H., On a system of differential equations leading to periodic functions, Acta Math. 27(1903)135-156.
    • (1903) Acta Math. , vol.27 , pp. 135-156
    • Baker, H.1
  • 10
    • 0001209959 scopus 로고
    • Reduction for constrained variational problems and jifds
    • Bryant R. and Griffiths P., Reduction for constrained variational problems and jifds, Amer. J. Math. 108 (1986) 525-570.
    • (1986) Amer. J. Math. , vol.108 , pp. 525-570
    • Bryant, R.1    Griffiths, P.2
  • 14
    • 40849117068 scopus 로고    scopus 로고
    • Addition laws on jacobian varieties on plane algebraic curves
    • Buchstaber V. and Leykin D., Addition laws on jacobian varieties on plane algebraic curves, Proc. Steklov Inst. Math. 251 (2005) 1-72.
    • (2005) Proc. Steklov Inst. Math. , vol.251 , pp. 1-72
    • Buchstaber, V.1    Leykin, D.2
  • 15
    • 84867952360 scopus 로고    scopus 로고
    • Finite-gap solutions of the vortex filament equation: Isoperiodic deformations
    • Calini A. and Ivey T., Finite-gap solutions of the vortex filament equation: Isoperiodic deformations, J. Nonlinear Sci. 17 (2007) 527-567.
    • (2007) J. Nonlinear Sci. , vol.17 , pp. 527-567
    • Calini, A.1    Ivey, T.2
  • 16
    • 56949088567 scopus 로고    scopus 로고
    • The stochastic elastica and excluded-volume perturbations of DNA conformational ensembles
    • Chirikjian G., The stochastic elastica and excluded-volume perturbations of DNA conformational ensembles, Int. J. Non-Linear Mech. 43 (2008) 1108-1120.
    • (2008) Int. J. Non-Linear Mech. , vol.43 , pp. 1108-1120
    • Chirikjian, G.1
  • 18
    • 0034364977 scopus 로고    scopus 로고
    • Quasiperiodic and periodic solutions for vector nonlinear schrödinger equations
    • Eilbeck J., Enolskii V. and Kostov N., Quasiperiodic and periodic solutions for vector nonlinear schrödinger equations, J. Math. Phys. 41 (2000) 8236-8254.
    • (2000) J. Math. Phys. , vol.41 , pp. 8236-8254
    • Eilbeck, J.1    Enolskii, V.2    Kostov, N.3
  • 21
    • 34250674162 scopus 로고    scopus 로고
    • Analogy between a vortex-jet filament and the Kirchhoff elastic rod
    • DOI 10.1016/j.fluiddyn.2006.12.004, PII S0169598307000251
    • Fukumoto Y., Analogy Between a Vortex-jet Filament and the Kirchhoff Elastic Rod, Fluid Dyn. Res. 39(2007) 511-520. (Pubitemid 46930789)
    • (2007) Fluid Dynamics Research , vol.39 , Issue.7 , pp. 511-520
    • Fukumoto, Y.1
  • 23
    • 0009276802 scopus 로고    scopus 로고
    • Œuvres Mathématiques d'Évariste Galois
    • Galois E., Œuvres Mathématiques d'Évariste Galois, J. de math, pures et appliquées 11 (1846) 381-444,
    • J. de Math, Pures et Appliquées , vol.11 , Issue.1846 , pp. 381-444
    • Galois, E.1
  • 24
    • 84874888567 scopus 로고    scopus 로고
    • tranlated into Japanese by Asakura-shoten, Tokyo
    • (tranlated into Japanese by Takase M, Abel/Galois Elliptic Functions. Asakura-shoten, Tokyo, 1998).
    • (1998) Abel/Galois Elliptic Functions
    • Takase, M.1
  • 25
    • 0001678450 scopus 로고
    • The korteweg-de vries hierarchy as dynamics of closed curves in the plane
    • Goldstein R. and Petrich D., The korteweg-de vries hierarchy as dynamics of closed curves in the plane, Phys. Rev. Lett. 67 (1991) 3203-3206.
    • (1991) Phys. Rev. Lett. , vol.67 , pp. 3203-3206
    • Goldstein, R.1    Petrich, D.2
  • 26
    • 84855854783 scopus 로고    scopus 로고
    • Extremals of the generalized euler-bernoulli energy and applications
    • Garay O., Extremals of the generalized euler-bernoulli energy and applications, J. Geom. Symm. Phys. 12(2008) 27-61.
    • (2008) J. Geom. Symm. Phys. , vol.12 , pp. 27-61
    • Garay, O.1
  • 27
    • 71449117434 scopus 로고    scopus 로고
    • The history of the planar elastica: Insights into mechanics and scientific method
    • Goss V., The history of the planar elastica: insights into mechanics and scientific method, Sci. & Educ. 18(2009)1057-1082.
    • (2009) Sci. & Educ. , vol.18 , pp. 1057-1082
    • Goss, V.1
  • 28
    • 84974277983 scopus 로고
    • A soliton on a vortex filament
    • Hasimoto H., A soliton on a vortex filament, J. Fluid Mech. 51 (1972) 477-485.
    • (1972) J. Fluid Mech. , vol.51 , pp. 477-485
    • Hasimoto, H.1
  • 29
    • 45149104274 scopus 로고
    • J. Dieudonné (Ed), Hermann, Paris, 1978 translated into Japanese by K. Ueno, N. Kaneko, Y. Namikawa, Y. Morita and J. Yamashita, Iwanami, Tokyo
    • Houzel C., Abrég'e d'histoire des mathématiques, vols. 1&2, J. Dieudonné (Ed), Hermann, Paris, 1978 (translated into Japanese by K. Ueno, N. Kaneko, Y. Namikawa, Y. Morita and J. Yamashita, Iwanami, Tokyo 1985).
    • (1985) Abrég'e D'histoire des Mathématiques , vol.1-2
    • Houzel, C.1
  • 30
    • 1642643945 scopus 로고
    • Üeber die entwicklungscoefficienten der lemniscratischen functioned
    • Hurwitz A., Üeber die entwicklungscoefficienten der lemniscratischen functioned Math. Ann. 51 (1899) 196-226.
    • (1899) Math. Ann. , vol.51 , pp. 196-226
    • Hurwitz, A.1
  • 31
    • 0001323002 scopus 로고
    • On the modified korteweg-de vries soliton equation and the loop soliton
    • Isimori Y., On the modified korteweg-de vries soliton equation and the loop soliton, J. Phys. Soc. Japan 50(1981)2471-2472.
    • (1981) J. Phys. Soc. Japan , vol.50 , pp. 2471-2472
    • Isimori, Y.1
  • 32
    • 47949108125 scopus 로고    scopus 로고
    • Kirchhoff elastic rods in three-dimensional space forms
    • Kawakubo S., Kirchhoff elastic rods in three-dimensional space forms, J. Math. Soc. Japan 60 (2008) 551-582.
    • (2008) J. Math. Soc. Japan , vol.60 , pp. 551-582
    • Kawakubo, S.1
  • 33
    • 0000704596 scopus 로고
    • Statistical mechanics of semiflexible polymers: Yesterday, today and tomorrow
    • Kholodenko A., Statistical mechanics of semiflexible polymers: Yesterday, today and tomorrow, J. Chem. Soc. Faraday Trans. 91 (1995) 2473-2482.
    • (1995) J. Chem. Soc. Faraday Trans. , vol.91 , pp. 2473-2482
    • Kholodenko, A.1
  • 34
    • 0040590366 scopus 로고
    • Classical dynamics of the rigid string from the willmore functional
    • Kholodenko A. and Nesterenko V., Classical dynamics of the rigid string from the willmore functional, J. Geom. Phys. 16 (1995) 15-26.
    • (1995) J. Geom. Phys. , vol.16 , pp. 15-26
    • Kholodenko, A.1    Nesterenko, V.2
  • 35
    • 84930244279 scopus 로고
    • Über das gleichgewicht und die bewegung einer elastischen scheibe
    • Kirchhoff G., Über das gleichgewicht und die bewegung einer elastischen scheibe, J. für reine und angew. math. 40(1850)51-88.
    • (1850) J. für Reine und Angew. Math. , vol.40 , pp. 51-88
    • Kirchhoff, G.1
  • 37
    • 0040446609 scopus 로고
    • Über hyperelliptische sigmafunetionen
    • Klein F., Über hyperelliptische sigmafunetionen, Math. Ann. 32(1888) 351-380.
    • (1888) Math. Ann. , vol.32 , pp. 351-380
    • Klein, F.1
  • 38
    • 0000547647 scopus 로고
    • A loop soliton propagating along a streched rope
    • Konno K., Ichikawa Y and Wadati M., A loop soliton propagating along a streched rope, J. Phys. Soc. Jpn. 50 (1981) 1025-1026.
    • (1981) J. Phys. Soc. Jpn. , vol.50 , pp. 1025-1026
    • Konno, K.1    Ichikawa, Y.2    Wadati, M.3
  • 39
    • 0009801376 scopus 로고    scopus 로고
    • Weierstrass representations for surfaces in 4D spaces and thier integrable dynamics via the DS hierarchy
    • Konopelchenko B., Weierstrass representations for surfaces in 4D spaces and thier integrable dynamics via the DS hierarchy, Ann. Global Anal. Geom. 18(2000) 61-74.
    • (2000) Ann. Global Anal. Geom. , vol.18 , pp. 61-74
    • Konopelchenko, B.1
  • 41
    • 84972507666 scopus 로고
    • The total squared curvature of closed curves
    • Langer J. and Singer D., The total squared curvature of closed curves, J. Diff. Geom. 20 (1984) 1-22.
    • (1984) J. Diff. Geom. , vol.20 , pp. 1-22
    • Langer, J.1    Singer, D.2
  • 42
    • 77954940293 scopus 로고    scopus 로고
    • EECS Department, University of California, Berkeley, UCB/EECS-2008-103
    • Levien R., The Elastica: A Mathematical History, EECS Department, University of California, Berkeley, UCB/EECS-2008-103 2008 http://www.eecs. berkeley.edu/Pubs/TechRpts/2008/EECS-2008-103.html.
    • (2008) The Elastica: A Mathematical History
    • Levien, R.1
  • 43
    • 0030797236 scopus 로고    scopus 로고
    • Atomic force microscopic demonstration of DNA looping by GalR and HU
    • DOI 10.1093/nar/25.4.873
    • Lyubchenko Y., Shlyakhtenko L., Aki T. and Adhya S., Atomic Force Microscopic Demonstration of DNA Looping GalR and HU, Nucl. Acids Research 25(1997) 873-876. (Pubitemid 27299846)
    • (1997) Nucleic Acids Research , vol.25 , Issue.4 , pp. 873-876
    • Lyubchenko, Y.L.1    Shlyakhtenko, L.S.2    Aki, T.3    Adhya, S.4
  • 44
    • 0009219595 scopus 로고
    • On the physical relation between the dirac equation and the generalized mKdV equation on a thin elastic rod
    • Matsutani S., On the physical relation between the dirac equation and the generalized mKdV equation on a thin elastic rod, Phys. Lett. A 189 (1994) 27-31.
    • (1994) Phys. Lett. A , vol.189 , pp. 27-31
    • Matsutani, S.1
  • 45
    • 0010763162 scopus 로고
    • The relation of lemniscate and a loop soliton as 3/2 and I spin fields along the modified korteweg-de vries equation
    • Matsutani S., The relation of lemniscate and a loop soliton as 3/2 and I spin fields along the modified korteweg-de vries equation, Mod. Phys. Lett. A 10(1995) 717-721.
    • (1995) Mod. Phys. Lett. A , vol.10 , pp. 717-721
    • Matsutani, S.1
  • 46
    • 0040686988 scopus 로고
    • The physical realization of the jimbo-miwa theory of the modified korteweg-de vries equation on a thin elastic rod: Fermionic theory
    • Matsutani S., The physical realization of the jimbo-miwa theory of the modified korteweg-de vries equation on a thin elastic rod: Fermionic theory, Int. J. Mod. Phys. A 10(1995) 3091-3107.
    • (1995) Int. J. Mod. Phys. A , vol.10 , pp. 3091-3107
    • Matsutani, S.1
  • 47
    • 0032549423 scopus 로고    scopus 로고
    • Statistical mechanics of elastica on a plane: Origin of the MKdV hierarchy
    • PII S0305447098834306
    • Matsutani S., Statistical Mechanics of Elastica on Plane: Origin of MKdV Hierarchy, J. Phys. A Math. & Gen. 31 (1998) 2705-2725. (Pubitemid 128382170)
    • (1998) Journal of Physics A: Mathematical and General , vol.31 , Issue.11 , pp. 2705-2725
    • Matsutani, S.1
  • 49
    • 0033074827 scopus 로고    scopus 로고
    • Statistical mechanics of non-stretching elástica in three dimensional space
    • Matsutani S., Statistical mechanics of non-stretching elástica in three dimensional space, J. Geom. Phys. 29 (1999) 243-259.
    • (1999) J. Geom. Phys. , vol.29 , pp. 243-259
    • Matsutani, S.1
  • 51
    • 0036331647 scopus 로고    scopus 로고
    • Hyperelliptic loop solitons with genus g: Investigation of a quantized elastica
    • Matsutani S., Hyperelliptic loop solitons with genus g: Investigation of a quantized elastica, J. Geom. Phys. 43 (2002) 146-162.
    • (2002) J. Geom. Phys. , vol.43 , pp. 146-162
    • Matsutani, S.1
  • 52
    • 38949095554 scopus 로고    scopus 로고
    • On a relation of weierstras al-functions
    • Matsutani S., On a relation of weierstras al-functions, Int. J. Appl. Math. 11 (2002) 295-307.
    • (2002) Int. J. Appl. Math. , vol.11 , pp. 295-307
    • Matsutani, S.1
  • 53
    • 34250686230 scopus 로고    scopus 로고
    • Reality conditions of loop solitons genus g: Hyperelliptic am functions
    • Matsutani S., Reality conditions of loop solitons genus g: Hyperelliptic am functions, Electron. J. Diff. Eqns. 2007(2007) 1-12.
    • (2007) Electron. J. Diff. Eqns. , vol.2007 , pp. 1-12
    • Matsutani, S.1
  • 54
    • 34249727416 scopus 로고    scopus 로고
    • Generalized weierstrass relations and frobenius reciprocity
    • Matsutani, S., Generalized weierstrass relations and frobenius reciprocity, Math. Phys. Anal. Geom. 9 (2007) 353-369.
    • (2007) Math. Phys. Anal. Geom. , vol.9 , pp. 353-369
    • Matsutani, S.1
  • 56
    • 38949162166 scopus 로고    scopus 로고
    • Relations in a quantized elastica
    • 075201
    • Matsutani S., Relations in a quantized elastica, J. Phys. A: Math.& Theor. 41 (2008) 075201 (12pp).
    • (2008) J. Phys. A: Math.& Theor. , vol.41 , pp. 12
    • Matsutani, S.1
  • 57
    • 0141705194 scopus 로고    scopus 로고
    • On the moduli of a quantized elastica in P and KdV flows: Study of hyperelliptic curves as an extension of Euler's perspective of elastica I
    • DOI 10.1142/S0129055X03001722
    • Matsutani S. and Onishi Y., On the Moduli of a Quantized Elastica in P and KdV Flows: Study of Hyperelliptic Curves as an Extension of Euler's Perspective of Elastica I, Rev. Math. Phys. 15 (2003) 559-628. (Pubitemid 37215277)
    • (2003) Reviews in Mathematical Physics , vol.15 , Issue.6 , pp. 559-628
    • Matsutani, S.1    Onishi, Y.2
  • 58
    • 0011892813 scopus 로고
    • Physical relation between quantum mechanics and soliton on a thin elastic rod
    • Matsutani S. and Tsuru H., Physical relation between quantum mechanics and soliton on a thin elastic rod, Phys. Rev. A 46(1992) 1144-1147.
    • (1992) Phys. Rev. A , vol.46 , pp. 1144-1147
    • Matsutani, S.1    Tsuru, H.2
  • 61
    • 0002651956 scopus 로고
    • Elástica and computer vision
    • C. Bajaj (Ed), Springer, Berlin
    • Mumford D., Elástica and computer vision, In: Algebraic Geometry and its Applications, C. Bajaj (Ed), Springer, Berlin, 1993 pp 507-518.
    • (1993) Algebraic Geometry and Its Applications , pp. 507-518
    • Mumford, D.1
  • 62
    • 0030748230 scopus 로고    scopus 로고
    • Nonlinear dynamics of solitary waves in an extensible rod
    • Nishinari K., Nonlinear dynamics of solitary waves in an extensible rod, Proc. R. Soc. Lond. A 453 (1997) 817-833.
    • (1997) Proc. R. Soc. Lond. A , vol.453 , pp. 817-833
    • Nishinari, K.1
  • 67
    • 42149106141 scopus 로고    scopus 로고
    • Maxwell strata in the euler elastic problem
    • Sachkov Y, Maxwell strata in the euler elastic problem, J. Dynamical and Control Systems 14 (2008) 169-234.
    • (2008) J. Dynamical and Control Systems , vol.14 , pp. 169-234
    • Sachkov, Y.1
  • 69
    • 33847283464 scopus 로고    scopus 로고
    • Variational discretization of euler's elástica problem
    • Sogo K., Variational discretization of euler's elástica problem, J. Phys. Soc. Japan 75 (2006) 064007.
    • (2006) J. Phys. Soc. Japan , vol.75 , pp. 064007
    • Sogo, K.1
  • 70
    • 33746366182 scopus 로고    scopus 로고
    • Two-dimensional Dirac operator and the theory of surfaces
    • DOI 10.1070/RM2006v061n01ABEH004299
    • Taimanov I., Two-Dimensional Dirac Operator and the Theory of Surfaces, Russian Math. Suveys 61(2006) 79-159. (Pubitemid 44109592)
    • (2006) Russian Mathematical Surveys , vol.61 , Issue.1 , pp. 79-159
    • Taimanov, I.A.1
  • 74
    • 34250383456 scopus 로고
    • History of classical mechanics part ii the 19th and 20th centuries
    • Truesdell C., History of classical mechanics part ii the 19th and 20th centuries, Die Naturwissenschaften 63(1976)119-130.
    • (1976) Die Naturwissenschaften , vol.63 , pp. 119-130
    • Truesdell, C.1
  • 75
    • 84968511025 scopus 로고
    • The influence of elasticity on analysis: The classic heritage
    • Truesdell C., The influence of elasticity on analysis: The classic heritage, Bull. Amer. Math. Soc. 9 (1983) 293-310.
    • (1983) Bull. Amer. Math. Soc. , vol.9 , pp. 293-310
    • Truesdell, C.1
  • 76
    • 0004895024 scopus 로고
    • Equilibrium shapes and vibrations of thin elastic rod
    • Tsuru H., Equilibrium shapes and vibrations of thin elastic rod, J. Phys. Soc. Japan 56 (1987) 2309-2324.
    • (1987) J. Phys. Soc. Japan , vol.56 , pp. 2309-2324
    • Tsuru, H.1
  • 77
    • 0022816976 scopus 로고
    • Elastic model of highly supercoiled DNA
    • Tsuru H. and Wadati M., Elastic model of highly supercoiled DNA, Biopolymers 25(1986) 2083-2096.
    • (1986) Biopolymers , vol.25 , pp. 2083-2096
    • Tsuru, H.1    Wadati, M.2
  • 78
    • 56549102886 scopus 로고    scopus 로고
    • Cylindrical equilibrium shapes of fluid membranes
    • 435201
    • Vassilev V., Djondjorov P. and Mladenov I., Cylindrical equilibrium shapes of fluid membranes, J. Phys. A 41(2008) 435201(16pp).
    • (2008) J. Phys. A , vol.41 , pp. 16
    • Vassilev, V.1    Djondjorov, P.2    Mladenov, I.3
  • 79
    • 0010667117 scopus 로고    scopus 로고
    • Plane domains which are spectrally determined
    • Watanabe K, Plane domains which are spectrally determined, Ann. Global. Anal. Geom. 18 (2000) 447-475.
    • (2000) Ann. Global. Anal. Geom. , vol.18 , pp. 447-475
    • Watanabe, K.1
  • 80
    • 0242337898 scopus 로고
    • Zur théorie der Abel'schen functionen
    • in Mathematische Werke I, Mayer und Müller, Berlin
    • Weierstrass K., Zur théorie der Abel'schen functionen, Aus dem Crelle'schen Journal 47 (1854) in Mathematische Werke I, Mayer und Müller, Berlin, 1894.
    • (1894) Aus Dem Crelle'schen Journal , vol.47 , Issue.1854
    • Weierstrass, K.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.