Resources, Readings, and References#

Textbook#

References#

Arnold89

Vladimir I. Arnol'd. Mathematical Methods of Classical Mechanics. Volume 60 of Graduate Texts in Mathematics. Springer-Verlag, New York, 2 edition, 1989. ISBN 978-1-4757-2063-1. translated by K. Vogtmann and A. Weinstein. doi:10.1007/978-1-4757-2063-1.

BB12

Thomas E. Baker and Andreas Bill. Jacobi elliptic functions and the complete solution to the bead on the hoop problem. Amer. J. Phys., 80(6):506–514, June 2012. doi:10.1119/1.3682321.

BDJS14

Silas R. Beane, Zohreh Davoudi, and Martin J. Savage. Constraints on the universe as a numerical simulation. The European Physical Journal A, 50(9):148, 2014. URL: https://doi.org/10.1140/epja/i2014-14148-0, doi:10.1140/epja/i2014-14148-0.

Boy15

John P. Boyd. Four ways to compute the inverse of the complete elliptic integral of the first kind. Comp. Phys. Comm., 196:13–18, November 2015. doi:10.1016/j.cpc.2015.05.006.

BFJ+18

Aurel Bulgac, Michael McNeil Forbes, Shi Jin, Rodrigo Navarro Perez, and Nicolas Schunck. Minimal nuclear energy density functional. Phys. Rev. C, 97:044313, April 2018. arXiv:1708.08771, doi:10.1103/PhysRevC.97.044313.

CDM06

Pierre Cartier and Cecile DeWitt-Morette. Functional Integration: Action and Symmetries. Cambridge Monographs on Mathematical Physics. Cambridge University Press, 2006. ISBN 9780511535062. URL: http://dx.doi.org/10.1017/CBO9780511535062, doi:10.1017/cbo9780511535062.

CM00

Alexandre J. Chorin and Jerrold E. Marsden. A Mathematical Introduction to Fluid Mechanics. Volume 4 of Texts in Applied Mathematics. Springer New York, New York, NY, UNITED STATES, 3 edition, 2000. ISBN 9781461208839. doi:10.1007/978-1-4612-0883-9.

CT91

E. M. F. Curado and C. Tsallis. Generalized statistical mechanics: connection with thermodynamics. J. Phys. A, 24:L69–L72, 1991.

DM76

Cécile DeWitt-Morette. The semiclassical expansion. Ann. Phys. (NY), 97(2):367–399, April 1976. doi:10.1016/0003-4916(76)90041-5.

Fei78

Mitchell J. Feigenbaum. Quantitative universality for a class of nonlinear transformations. Journal of Statistical Physics, 19(1):25–52, July 1978. URL: https://doi.org/10.1007%2Fbf01020332, doi:10.1007/bf01020332.

FW03

Alexander L. Fetter and John Dirk Walecka. Theoretical Mechanics of Particles and Continua. Dover, 2003. ISBN 978-0486432618.

FW06

Alexander L. Fetter and John Dirk Walecka. Nonlinear Mechanics: A Supplement to Theoretical Mechanics of Particles and Continua. Dover Publications, Mineola, New York, 2006. ISBN 978-0486450315.

GPS00

Herbert Goldstein, Charles Poole, and John Safko. Classical Mechanics. Addison Wesley, Reading, Mass., 3 edition, 2000.

Hou20

Bahram Houchmandzadeh. The hamilton–jacobi equation: an alternative approach. Amer. J. Phys., 88(5):353–359, 2020. URL: https://doi.org/10.1119/10.0000781, arXiv:1910.09414, doi:10.1119/10.0000781.

Jen11

Jens Hoejgaard Jensen. Rules for rolling as a rotation about the instantaneous point of contact. Eur. J. Phys., 32(2):389–397, January 2011. doi:10.1088/0143-0807/32/2/012.

LL76

L. D. Landau and E. M. Lifshitz. Mechanics. Volume 1 of Course of Theoretical Physics. Butterworth-Heinemann, Oxford, third edition edition, 1976. ISBN 978-0-7506-2896-9. doi:10.1016/B978-0-08-050347-9.50006-X.

Mer07

N. D. Mermin. Quantum Computer Science: An Introduction. Cambridge University Press, 2007. ISBN 978-0-511-33982-0. URL: https://www.cambridge.org/core/books/quantum-computer-science/66462590D10C8010017CF1D7C45708D7, doi:10.1017/CBO9780511813870.

ML03

Cleve Moler and Charles Van Loan. Nineteen dubious ways to compute the exponential of a matrix, twenty-five years later. SIAM Review, 45(1):3–49, 2003. URL: http://dx.doi.org/10.1137/S00361445024180, doi:10.1137/S00361445024180.

NC10

Michael A. Nielsen and Isaac L. Chuang. Quantum Computation and Quantum Information. Cambridge University Press, 2010. URL: https://doi.org/10.1017%2Fcbo9780511976667, doi:10.1017/cbo9780511976667.

PR82

Ian Percival and Derek Richards. Introduction to Dynamics. Cambridge University Press, Cambridge; New York, 1982. ISBN 0521281490.

Sew02

Geoffrey L. Sewell. Quantum Mechanics and Its Emergent Macrophysics. Princeton University Press, Princeton, New Jersey, 2002. doi:10.2307/j.ctv173f2jj.

Sha94

R. Shankar. Principles of Quantum Mechanics. Springer US, 1994. URL: https://doi.org/10.1007%2F978-1-4757-0576-8, doi:10.1007/978-1-4757-0576-8.

SW15

G. J. Sussman and J. Wisdom. Structure and Interpretation of Classical Mechanics. MIT, Cambridge, MA, 2015. ISBN 9780262028967.

Tsa88

Constantino Tsallis. Possible generalization of boltzmann-gibbs statistics. J. Stat. Phys., 52:479–487, 1988.

TBCP03

Constantino Tsallis, Fulvio Baldovin, Roberto Cerbino, and Paolo Pierobon. Introduction to nonextensive statistical mechanics and thermodynamics. In The Physics of Complex Systems: New Advances & Perspectives. July 2003. arXiv:cond-mat/0309093.

TB04

Constantino Tsallis and Edgardo Brigatti. Nonextensive statistical mechanics: a brief introduction. Continuum Mech. Thermodyn., pages 223–235, 2004. arXiv:cond-mat/0305606.

TT10

Leaf Turner and Ari M. Turner. Asymmetric rolling bodies and the phantom torque. Amer. J. Phys., 78(9):905–908, September 2010. URL: https://doi.org/10.1119%2F1.3456118, doi:10.1119/1.3456118.

ValleeS10

Olivier Vallée and Manuel Soares. Airy Functions and Applications to Physics. Imperial College Press, 2 edition, June 2010. ISBN 9781848165489. doi:10.1142/p709.

WS06

Clive G Wells and Stephen T C Siklos. The adiabatic invariance of the action variable in classical dynamics. Eur. J. Phys., 28(1):105–112, December 2006. URL: http://dx.doi.org/10.1088/0143-0807/28/1/011, arXiv:physics/0610084, doi:10.1088/0143-0807/28/1/011.

Linear Algebra#