Path-Independence of Work Done Theorem Is Invalid in Center-Bound Force Fields
Abstract
Abstract: The notion of work done, and the corresponding to it concept of potential energy, was incompletely defined making the path independence theorem of work done by center-bound force fields invalid for other than radial/conservative forces. Hence nonradial effects along equipotential surfaces, whose presence was suggested by experiments, can exist. New, mathematically complete representation of work done by center-bound force fields (generated by a single source) is offered.
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Anton, H. (1999). Calculus: A new horizon. New York: Wiley, p.1080f.
Barr, T. H. (1997). Vector calculus. Upper Saddle River, NJ: Prentice-Hall.
Basu, D. (1998). Radius of the sun in relation to solar activity. Solar Phys., 183, 291-294.
Beatrous, F., & Curjel, C. R. (2002). Multivariable calculus. A geometric approach. Upper Saddle River, NJ: Prentice Hall.
Beiser, A. (1973). Concepts of modern physics. New York: McGraw-Hill.
Bers, L. (1967). Calculus I. New York: Holt, Rinehart and Winston.
Birkhoff, G. (Ed.) (1973). A source book in classical analysis. Cambridge, MA: Harvard University Press.
Capra, F. (1975). The Tao of physics. Boston: Shambhala.
Cartan, E. (1984c). Les récents généralisations de la notion d’espace [Recent generalizations of the notion of space]. In E. Cartan (Ed.), Œuvres complètes. Part 3.1 (pp.863-889). Paris: Éditions du CNRS.
Cartan, E. (1984a). Notice historique sur la notion de parallélisme absolu [Historical note on the concept of absolute parallelism]. In E. Cartan (Ed.), Œuvres complètes Part 3.2 (pp.1121-1129). Paris: Éditions du CNRS.
Cartan, E. (1984b). Sur la connexion affine des surfaces [The affine connection surfaces]. In E. Cartan (Ed.), Œuvres complètes. Part 3.1.( pp.909-912). Paris: Éditions du CNRS.
Cartan, E. (1986). On manifolds with an affine connection and the general theory of relativity. Napoli: Bibliopolis.
Chirgwin, B. H., & Plumpton, C. (1964). A course of mathematics for engineers and scientists 4. New York: Macmillan.
Corben, H. C. & Stehle, P. (1950). Classical mechanics. New York: Wiley.
Cronin-Scanlon, J. (1967). Advanced calculus. Boston: Heath.
Czajko, J. (1990). On the Hafele-Keating experiment. Ann. Phys. (Leipzig), 47, 517-518.
Czajko, J. (1991). Experiments with flying atomic clocks. Exper. Tech. Phys., 39, 145-147.
Czajko, J. (2000). On conjugate complex time II: Equipotential effect of gravity retrodicts differential and predicts apparent anomalous rotation of the Sun. Chaos, Solit. Fract. 11, 2001-2016.
Czajko, J. (2011). Radial and nonradial effects in Frenet frame. Appl. Phys. Res., 3(1), 2-7.
Doran, C., Lasenby, A., & Gul, S. (1993). Imaginary numbers are not real– the geometric algebra of spacetime. Found. Phys., 23(9), 1175-1201.
Dyson, F. (1921). Relativity and the eclipse observation of May 1919. Nature, 106, 786-787.
Edwards, C. H., & Penney, D. E. (1999). Multivariable calculus with analytic geometry. Upper Saddle River, NJ: Prentice-Hall.
Edwards, C. H., & Penney, D. E. (2002). Calculus. Upper Saddle River, NJ: Prentice-Hall.
Einstein, A. (1916). The foundations of the general theory of relativity. In H. A. Lorentz, et al. (Ed.), The principle of relativity (pp.111-164). New York: Dover.
Einstein, A. (1948). A generalized theory of gravitation. Rev. Mod. Phys., 20, 35-39.
Eisenman, R. L. (2005). Matrix vector analysis. Mineola, NY: Dover.
Feynman, R. P., Leighton, R. B., & Sands, M. (1977). The Feynman lectures on physics I: Mainly mechanics, radiation and heat. Reading, MA: Addison-Wesley.
Finney, R. L., Thomas, G. B., Demana, F., & Waits, B. K. (1995). Calculus: Graphical, numerical, algebraic. Single variable version. Reading, MA: Addison-Wesley.
Fitzpatrick, P. M. (1996). Advanced calculus: A course in mathematical analysis. Boston: PWS.
Gigolashvili, M. S., Gogoladze, N. A., & Khutsishvili, E. V. (1995). Revealing of periodicities in the variations of differential rotation of the Sun. Astron. Nachr., 316(5), 285-290.
Halliday, D., & Resnick, R. (1974). Fundamentals of physics. New York: Wiley.
Hart, W. L. (1955). Calculus. Boston: Heath.
Heitsch, W. (1978). Mathematik und Weltanschaung [Mathematics and worldview]. Berlin: Akademie-Verlag.
Hughes-Hallett, D., McCallum, W. G., Gleason, A. M., Flath, D. E, Lock, P. F., Gordon, S. P., …Tucker, T. W. (2005). Calculus. Single and multivariable. Hoboken, NJ: Wiley.
Jaeger, J. C. (1951). An introduction to applied mathematics. Oxford: Clarendon Press.
Johnson, J. L. (1999). On magnetohydrodynamic equilibrium and stability in stellarators. Plasma Phys. Rep., 25(12), 1013-1023.
Larson, R. E., & Hostetler, R. P. (1986). Calculus with analytic geometry. Lexington, MA: Heath.
Lerner, R. G., & Trigg, G. L. (Eds.) (2005). Encyclopedia of physics I. Third, completely revised and enlarged edition. Weinheim: Wiley-VCH.
McCallum, W. G., et al. (2005). Multivariable calculus. Hoboken, NJ: Wiley.
Merat, P. (1974). Observed Deflection of Light by the Sun as a Function of Solar Distance. Astron. Astrophys., 32, 471-475.
Mercier, A. (1959). Analytical and canonical formalism in physics. Amsterdam: North-Holland.
Mercier, A. (1977). Speculative remarks on physics in general and relativity in particular. In V. De Sabbata & J. Weber (Eds.), Topics in theoretical and experimental gravitation physics (pp.295-303). London: Plenum Press.
Postnikov, M. M. (1983). The variational theory of geodesics. New York: Dover.
Ryder, L. H. (1996). Quantum field theory. Cambridge: Cambridge Univ. Press.
Sadeh, D., Knowles, S. H., & Yaplee, B. S. (1968). Search for a frequency shift of the 21-centimeter line from Taurus a near occultation by Sun. Science, 159, 307-308.
Sadeh, D., Knowles, S., & Au, B. (1968). The effect of mass on frequency. Science, 161, 567-569.
Salas, S. L., & Hille, E. (1990). Calculus: One and several variables. New York: Wiley.
Seaborn, J. B. (2001). Mathematics for the physical sciences. New York: Springer.
Stein, S. K., & Barcellos, A. (1992). Calculus and analytic geometry. New York: McGraw-Hill.
Stewart, J. (1999). Calculus: Early transcendentals. Pacific Grove, CA: Brooks/Cole.
Struik, D. J. (1988). Lectures on classical differential geometry. New York: Dover.
Swokowski, E. W. (1992). Calculus: Late trigonometry version. Boston: PWS.
Thomas, J. B., & Finney, R. L. (1996). Calculus and analytic geometry II. Reading, MA: Addison-Wesley.
Toretti, R. (1996). Relativity and geometry. New York: Dover.
Varberg, D., Purcell, E. J., & Rigdon, S. E. (2000). Calculus. Upper Saddle River, NJ: Prentice Hall.
Vyal’tsev, A. N. (1965). Discrete spacetime. Moscow. [in Russian].
Wenzl, A. (1954). Die philosophischen Grenzfragen der modernen Naturwissenschaft [The philosophical frontier issues of modern natural science]. Stuttgart: Kohlhammer Verlag.
Williams, J., Franklin, F. E., & Metcalfe, H. C. (1984). Modern physics. New York: Holt, Rinehart and Winston.
DOI: http://dx.doi.org/10.3968/j.sms.1923845220130702.2469
DOI (PDF): http://dx.doi.org/10.3968/g5279
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