Re-examining the law of energy conservation-A Euclidean geometric proof

Year 2025, Volume: 6 Issue: 1, 1 - 35, 30.01.2025

Alex Kımuya

https://doi.org/10.55696/ejset.1559047

Abstract

The law of energy conservation is a cornerstone of physics, limiting energy use and dictating the efficiency of thermodynamic processes. The primary objective of this paper is to challenge the traditional acceptance of the law of energy conservation as an unprovable axiom by presenting a novel, provable, and purely geometric approach within the framework of Euclidean geometry, thereby re-evaluating its theoretical and empirical foundations. Driven by the ongoing pursuit of solutions to energy crises, the paper critically examines attempts to disprove the law and the search for alternative energy sources. Contrary to prevailing beliefs, it posits two key viewpoints: the lack of rigorous proof establishing the law’s validity and the obscured motivations driving the invention of new energy sources. Highlighting the gap between theoretical acceptance and empirical evidence, the paper introduces a geometric framework to elucidate the empirical limitations and precision of energy conservation. Through this lens, it challenges the law’s universal applicability, particularly debunking the notion of perpetual motion machines as proof of its validity. The findings include a geometric and practical redefinition of isolated systems, a proof of Newton’s laws of motion, a geometric derivation of the Newtonian kinetic energy equation, and the demonstration of these geometric concepts’ practicality independent of experiments. These insights call for a re-evaluation of the traditional understanding of energy conservation and offer transformative implications for future energy exploration and innovation.

Keywords

Energy conservation, Thermodynamics, Energy, Perpetual motion, Descartes, Spinoza, Leibniz, Euclid, Inverse points, Euclidean geometry

References

• H. Goldstein, C. P. Poole, and J. L. Safko, Classical mechanics, 3. ed., [Nachdr.]. San Francisco Munich: Addison Wesley, 2008.
•      G. Kalies and D. D. Do, “Momentum work and the energetic foundations of physics. I. Newton’s laws of motion tailored to processes,” AIP Adv., vol. 13, no. 6, p. 065121, Jun. 2023, https://doi.org/10.1063/5.147910.
•      F. Verhulst, “Henri Poincaré (1854–1912) Engineer, Mathematician, Physicist and Philosopher,” in IUTAM Symposium on Exploiting Nonlinear Dynamics for Engineering Systems, vol. 37, I. Kovacic and S. Lenci, Eds., inIUTAM Bookseries, vol. 37. , Cham: Springer International Publishing, 2020, pp. 15–26. https://doi.org/10.1007/978-3-030-23692-2_2.
•      “Poincaré, Jules Henri | Internet Encyclopedia of Philosophy.” Accessed: Jan. 10, 2025. [Online]. Available: https://iep.utm.edu/poincare/.
•      M. Silberstein, W. M. Stuckey, and T. McDevitt, “Beyond Causal Explanation: Einstein’s Principle Not Reichenbach’s,” Entropy, vol. 23, no. 1, p. 114, Jan. 2021, https://doi.org/10.3390/e23010114.
•      L. Guzzardi, “Energy, Metaphysics, and Space: Ernst Mach’s Interpretation of Energy Conservation as the Principle of Causality,” Sci. Educ., vol. 23, no. 6, pp. 1269–1291, Jun. 2014, https://doi.org/10.1007/s1119-1012-9542-9.
•      J. B. Pitts, “Conservation of Energy: Missing Features in Its Nature and Justification and Why They Matter,” Found. Sci., vol. 26, no. 3, pp. 559–584, Sep. 2021, https://doi.org/10.1007/s10699-020-09657-1.
•      N. Banerjee and S. Sen, “Einstein pseudotensor and total energy of the universe,” Pramana, vol. 49, no. 6, pp. 609–615, Dec. 1997, https://doi.org/10.1007/BF02848334.
•      L. Patton, “Experiment and theory building,” Synthese, vol. 184, no. 3, pp. 235–246, Feb. 2012, https://doi.org/10.1007/s11229-010-9772-9.
•    “Chapter 1: The Nature of Science.” Accessed: Jan. 10, 2025. [Online]. Available: https://www.project2061.org/publications/sfaa/online/chap1.htm?
•    P. Fara, “What Is Science? AHistorian’s Perplexities,” Mètode Rev. Difus. Investig., vol. 0, no. 5, Apr. 2015, https://doi.org/10.7203/metode.84.3915.
•    R. V. Blystone and K. Blodgett, “WWW: The Scientific Method,” CBE—Life Sci. Educ., vol. 5, no. 1, pp. 7–11, Mar. 2006, https://doi.org/10.1187/cbe.05-12-0134.
•    K. Morsanyi, T. McCormack, and E. O’Mahony, “The link between deductive reasoning and mathematics,” Think. Reason., vol. 24, no. 2, pp. 234–257, Apr. 2018, https://doi.org/10.1080/13546783.2017.1384760.
•    Liaqat Khan, “What is Mathematics - an Overview,” 2015, Unpublished. https://doi.org/10.13140/RG.2.1.3626.8967.
•    Jaydip Datta, “MATHEMATICS: An Inductive & Deductive Review,” 2022, https://doi.org/10.13140/RG.2.2.25473.99683/9.
•    B. Shea, “Karl Popper: Philosophy of Science,” 2016.
•    S. El-Badawy, “The Importance of Inductive Reasoning in Science: A Critical Analysis,” 2022, https://doi.org/10.13140/RG.2.2.18728.14087.
•    B. Hepburn and H. Andersen, “Scientific Method,” in The Stanford Encyclopedia of Philosophy, Summer 2021., E. N. Zalta, Ed., Metaphysics Research Lab, Stanford University, 2021. Accessed: Jan. 10, 2025. [Online]. Available: https://plato.stanford.edu/archives/sum2021/entries/scientific-method/.
•    R. Meer, “Immanuel Kant’s Theory of Objects and Its Inherent Link to Natural Science,” Open Philos., vol. 1, no. 1, pp. 342–359, Nov. 2018, https://doi.org/10.1515/opphil-2018-0025.
•    A. Botica, “Intended’ and ‘Experienced’ Meaning: Reevaluating the Reader-Response Theory,” J. Educ. Soc. Res., Oct. 2013, https://doi.org/10.5901/jesr.2013.v3n7p519.
•    H. Meyer-Ortmanns and T. Reisz, Principles of Phase Structures in Particle Physics, vol. 77. in World Scientific Lecture Notes in Physics, vol. 77. WORLD SCIENTIFIC, 2006. https://doi.org/10.1142/3763.
•    A. Szegleti and F. Márkus, “Dissipation in Lagrangian Formalism,” Entropy, vol. 22, no. 9, p. 930, Aug. 2020, https://doi.org/10.3390/e22090930.
•    D. Mušicki, “Extended Lagrangian formalism and the corresponding energy relations,” Eur. J. Mech. - ASolids, vol. 23, no. 6, pp. 975–991, Nov. 2004, https://doi.org/10.1016/j.euromechsol.2004.01.010.
•    R. M. Marinho, “Noether’s theorem in classical mechanics revisited,” Eur. J. Phys., vol. 28, no. 1, pp. 37–43, Jan. 2007, https://doi.org/10.1088/0143-0807/28/1/004.
•    K. Brading and E. Castellani, “SYMMETRIES AND INVARIANCES IN CLASSICAL PHYSICS,” in Philosophy of Physics, Elsevier, 2007, pp. 1331–1367. https://doi.org/10.1016/B978-044451560-5/50016-6.
•    S. Bilbao, M. Ducceschi, and F. Zama, “Explicit exactly energy-conserving methods for Hamiltonian systems,” J. Comput. Phys., vol. 472, p. 111697, Jan. 2023, https://doi.org/10.1016/j.jcp.2022.111697.
•    G. Kalies and D. D. Do, “Momentum work and the energetic foundations of physics. III. The unification of mechanics and electrodynamics,” AIP Adv., vol. 13, no. 9, p. 095322, Sep. 2023, https://doi.org/10.1063/5.0166847.
•    H. Liu, X. Cai, Y. Cao, and G. Lapenta, “An efficient energy conserving semi-Lagrangian kinetic scheme for the Vlasov-Ampère system,” J. Comput. Phys., vol. 492, p. 112412, Nov. 2023, https://doi.org/10.1016/j.jcp.2023.112412.
•    D. E. Chang, A. M. Bloch, N. E. Leonard, J. E. Marsden, and C. A. Woolsey, “The Equivalence of Controlled Lagrangian and Controlled Hamiltonian Systems,” ESAIM Control Optim. Calc. Var., vol. 8, pp. 393–422,2002https://doi.org/10.1051/cocv:2002045.
•    C. Woolsey, C. K. Reddy, A. M. Bloch, D. E. Chang, N. E. Leonard, and J. E. Marsden, “Controlled Lagrangian Systems with Gyroscopic Forcing and Dissipation,” Eur. J. Control, vol. 10, no. 5, pp. 478–496, Jan.2004https://doi.org/10.3166/ejc.10.478-496.
•    P. Holland, “Hamiltonian theory of wave and particle in quantum mechanics I. Liouville’s theorem and the interpretation of the de Broglie-Bohm theory,” Il Nuovo Cimento B, vol. 116, Sep. 2001.
•    V. Rastogi, A. Mukherjee, and A. Dasgupta, “A review on extension of Lagrangian-Hamiltonian mechanics,” J. Braz. Soc. Mech. Sci. Eng., vol. 33, no. 1, pp. 22–33, Mar. 2011, https://doi.org/10.1590/S1678-5878211000100004.
•    C. R. Galley, “Classical Mechanics of Nonconservative Systems,” Phys. Rev. Lett., vol. 110, no. 17, p. 174301, Apr. 2013, https://doi.org/10.1103/PhysRevLett.110.174301.
•    J.-T. Xing, “Generalised energy conservation law for chaotic phenomena,” Acta Mech. Sin., vol. 35, no. 6, pp. 1257–1268, Dec. 2019, https://doi.org/10.1007/s10409-019-00886-7.
•    R. Trudeau, “Euclidean Geometry,” 2001, pp. 22–105. https://doi.org/10.1007/978-1-4612-2102-9_2.
•    C. Sasaki, “The Géométrie of 1637,” in Descartes’s Mathematical Thought, vol. 237, in Boston Studies in the Philosophy of Science, vol. 237. , Dordrecht: Springer Netherlands, 2003, pp. 205–280. https://doi.org/10.1007/978-94-017-1225-5_6.
•    M. Panza, “Rethinking geometrical exactness,” Hist. Math., vol. 38, no. 1, pp. 42–95, Feb. 2011, https://doi.org/10.1016/j.hm.2010.09.001.
•    A. Ostermann and G. Wanner, “The Elements of Euclid,” in Geometry by Its History, in Undergraduate Texts in Mathematics. , Berlin, Heidelberg: Springer Berlin Heidelberg, 2012, pp. 27–59. https://doi.org/10.1007/97-83-642-29163-0_2.
•    R. Hartshorne, “Teaching Geometry According to Euclid,” Not. Am. Math. Soc., vol. 47, Jan. 2000.
•    A. M. Kimuya, “Constructability and Rigor of Angles Multiples of 3 in Euclidean Geometry,” Trends J. Sci. Res., vol. 2, no. 1, pp. 1–27, Jan. 2024, https://doi.org/10.31586/jml.2024.841.
•    N. F. Shul’ga, V. V. Syshchenko, A. I. Tarnovsky, V. I. Dronik, and A. Yu. Isupov, “Regular and chaotic motion domains in the channeling electron’s phase space and mean level density for its transverse motionenergy,” J. Instrum., vol. 14, no. 12, pp. C12022–C12022, Dec. 2019, https://doi.org/10.1088/1748-0221/14/12/C12022.
•    F. Borceux, “Euclid’s Elements,” in An Axiomatic Approach to Geometry, Cham: Springer International Publishing, 2014, pp. 43–110. https://doi.org/10.1007/978-3-319-01730-3_3.
•    R. J. Trudeau, “Euclidean Geometry,” in The Non-Euclidean Revolution, Boston, MA: Birkhäuser Boston, 2001, pp. 22–105. https://doi.org/10.1007/978-1-4612-2102-9_2.
•    P. Mancosu, “Descartes and Mathematics,” in A Companion to Descartes, John Wiley & Sons, Ltd, 2007, pp. 103–123. https://doi.org/10.1002/9780470696439.ch7.
•    G. Kalies, “Fundamental laws of nature confirmed by free fall,” Jun. 18, 2021. https://doi.org/10.21203/rs.3.rs-624477/v1.
•    L. Guzzardi, “Energy, Metaphysics, and Space: Ernst Mach’s Interpretation of Energy Conservation as the Principle of Causality,” Sci. Educ., vol. 23, no. 6, pp. 1269–1291, Jun. 2014, https://doi.org/10.1007/s-1119112-9542-9.
•    C. R. Palmerino, “Law of Free Fall in Renaissance Science,” in Encyclopedia of Renaissance Philosophy, M. Sgarbi, Ed., Cham: Springer International Publishing, 2019, pp. 1–7. https://doi.org/10.1007/978-3-319-2848-4_939-1.
•    E. Goren and I. Galili, “Newton’s Law - A Theory of motion or force?,” J. Phys. Conf. Ser., vol. 1287, no. 1, p. 012061, Aug. 2019, https://doi.org/10.1088/1742-6596/1287/1/012061.
•    J. Avigad, E. DEAN, and J. Mumma, “A Formal System for Euclid’S Elements,” Rev. Symb. Log., vol. 2, pp. 700–768, Dec. 2009, https://doi.org/10.1017/S1755020309990098.
•    M. Bunge, “Energy: Between Physics and Metaphysics,” Sci. Educ., vol. 9, no. 5, pp. 459–463, Sep. 2000, https://doi.org/10.1023/A:1008784424048.
•    P. Davies and N. H. Gregersen, Eds., Information and the Nature of Reality: From Physics to Metaphysics, 1st ed. Cambridge University Press, 2014. https://doi.org/10.1017/CBO9781107589056.
•    C. Annamalai and A. M. D. O. Siqueira, “Mass-Energy Equivalence derived from Newtonian mechanics,” J. Eng. Exact Sci., vol. 9, no. 8, pp. 15963–01e, Jun. 2023, https://doi.org/10.18540/jcecvl9iss8pp15963-01e.
•    G. D’Abramo, “Mass–energy connection without special relativity,” Eur. J. Phys., vol. 42, no. 1, p. 015606, Jan. 2020, https://doi.org/10.1088/1361-6404/abbca2.
•    B. Muhyedeen, “New Concept of Mass-Energy Equivalence,” Eur. J. Sci. Res., vol. ISSN 1450-216X Vol.26 No.2 (2009), pp.161–175, Feb. 2009.
•    R. Gobato, A. Gobato, and D. F. G. Fedrigo, “Energy and matter,” Sep. 02, 2015, arXiv: arXiv:1509.02892. https://doi.org/10.48550/arXiv.1509.02892.
•    C. Barreiro, J. M. Barreiro, J. A. Lara, D. Lizcano, M. A. Martínez, and J. Pazos, “The Third Construct of the Universe: Information,” Found. Sci., vol. 25, no. 2, pp. 425–440, Jun. 2020, https://doi.org/10.1007/s1699-019-09630-7.
•    T. R. Mongan, “Origin of the Universe, Dark Energy, and Dark Matter,” J. Mod. Phys., vol. 09, no. 05, pp. 832–850, 2018, https://doi.org/10.4236/jmp.2018.95054.
•    N. Raos, “Atomism in greek philosophy,” Kem. U Ind. Chem. Chem. Eng., vol. 51, pp. 385–392, Jan. 2002.
•    C. Masolo and L. Vieu, “Atomicity vs. Infinite Divisibility of Space,” in Spatial Information Theory. Cognitive and Computational Foundations of Geographic Information Science, vol. 1661, C. Freksa and D. M.Mark,Eds., in Lecture Notes in Computer Science, vol. 1661. , Berlin, Heidelberg: Springer Berlin Heidelberg, 1999, pp. 235–250. https://doi.org/10.1007/3-540-48384-5_16.
•    V. Villani, “The Way Ahead,” in Perspectives on the Teaching of Geometry for the 21st Century, vol. 5, C. Mammana and V. Villani, Eds., in New ICMI Study Series, vol. 5. , Dordrecht: Springer Netherlands, 1998, pp.319–327. https://doi.org/10.1007/978-94-011-5226-6_11.
•    A. Oliveira, “Coriolis’ Theory of Machines and Mechanisms,” Jan. 1980.
•    “Descartes, Rene | Internet Encyclopedia of Philosophy.” Accessed: Jan. 10, 2025. [Online]. Available: https://iep.utm.edu/rene-descartes/.
•    R. Descartes, The geometry of René Descartes. New York, NY: Dover Publications, 1996.
•    R. Hershkowitz et al., “Reasoning in Geometry,” in Perspectives on the Teaching of Geometry for the 21st Century, vol. 5, C. Mammana and V. Villani, Eds., in New ICMI Study Series, vol. 5. , Dordrecht: Springer Netherlands, 1998, pp. 29–83. https://doi.org/10.1007/978-94-011-5226-6_3.
•    D. Lomas, “Geometry starting with Euclid,” Can. J. Sci. Math. Technol. Educ., vol. 5, no. 2, pp. 271–276, Apr. 2005, https://doi.org/10.1080/14926150509556659.
•    W. Halbfaß, “Descartes, René: Principia philosophiae,” in Kindlers Literatur Lexikon (KLL), H. L. Arnold, Ed., Stuttgart: J.B. Metzler, 2020, pp. 1–3. https://doi.org/10.1007/978-3-476-05728-0_9540-1.
•    E. Mach, “ON THE PRINCIPLE OF THE CONSERVATION OF ENERGY,” The Monist, vol. 5, no. 1, pp. 22–54, 1894.
•    J.-P. Anfray, “Leibniz and Descartes,” in The Oxford Handbook of Descartes and Cartesianism, S. Nadler, T. M. Schmaltz, and D. Antoine-Mahut, Eds., Oxford University Press, 2019, pp. 720–737. https://doi.org/101093/oxfordhb/9780198796909.013.45.
•    Y. Kato and K. Sakamoto, “Between Cartesianism and orthodoxy: God and the problem of indifference in Christoph Wittich’s Anti-Spinoza,” Intellect. Hist. Rev., pp. 1–19, Dec. 2020, https://doi.org/10.1080/17496977.220.1852373.
•    G. E. Smith, “The vis viva dispute: A controversy at the dawn of dynamics,” Phys. Today, vol. 59, no. 10, pp. 31–36, Oct. 2006, https://doi.org/10.1063/1.2387086.
•    M. N. Hidayat, S. P. Chairandy, and F. Ronilaya, “Design and Analysis of A Perpetual Motion Machine Using Neodymium Magnets as A Prime Mover,” J. Southwest Jiaotong Univ., vol. 56, no. 2, pp. 211–219, Apr. 2021, https://doi.org/10.35741/issn.0258-2724.56.2.17.
•    S. V. Kukhlevsky, “Breaking of Energy Conservation Law: Creating and Destroying of Energy by Subwavelength Nanosystems,” 2006, arXiv. https://doi.org/10.48550/ARXIV.PHYSICS/061000.
•    J. F. Rodríguez-León, I. Cervantes, E. Castillo-Castañeda, G. Carbone, and D. Cafolla, “Design and Preliminary Testing of a Magnetic Spring as an Energy-Storing System for Reduced Power Consumption of a Humanoid Arm,” Actuators, vol. 10, no. 6, p. 136, Jun. 2021, https://doi.org/10.3390/act10060136.
•    A. P. David, “Electro-Magnetic Induction: Free Electricity Generator,” May 18, 2017, Social Science Research Network, Rochester, NY: 3486740. https://doi.org/10.2139/ssrn.3486740.
•    N. Coppedge, “TOP PERPETUAL MOTION MACHINES,” May 2022.
•    M. S. Berman, “On the Zero-Energy Universe,” Int. J. Theor. Phys., vol. 48, no. 11, pp. 3278–3286, Nov. 2009, https://doi.org/10.1007/s10773-009-0125-8.
•    M. Berman, “On the Zero-Energy Universe,” Int. J. Theor. Phys., vol. 48, May 2006, https://doi.org/10.1007/s10773-009-0125-8.
•    “Descartes, Rene: Scientific Method | Internet Encyclopedia of Philosophy.” Accessed: Jul. 16, 2022. [Online]. Available: https://iep.utm.edu/rene-descartes-scientific-method/.
•    J. F. Scott, The scientific work of René Descartes (1596-1650). in Routledge library editions: René Descartes, no. volume 3. London: Routledge, 2017.
•    A. Micheli and P. Iturralde, “[On the evolution of scientific thought],” Arch. Cardiol. Mex., vol. 85, Aug. 2015, https://doi.org/10.1016/j.acmx.2015.06.003.
•    Y. Guan et al., “Burden of the global energy price crisis on households,” Nat. Energy, vol. 8, no. 3, Art. no. 3, Mar. 2023, https://doi.org/10.1038/s41560-023-01209-8.
•    M. Farghali et al., “Strategies to save energy in the context of the energy crisis: a review,” Environ. Chem. Lett., vol. 21, no. 4, pp. 2003–2039, Aug. 2023, https://doi.org/10.1007/s10311-023-01591-5.
•    J. Mitali, S. Dhinakaran, and A. A. Mohamad, “Energy storage systems: a review,” Energy Storage Sav., vol. 1, no. 3, pp. 166–216, Sep. 2022, https://doi.org/10.1016/j.enss.2022.07.002.
•    R. Machotka, “Euclidean Model of Space and Time,” J. Mod. Phys., vol. 09, pp. 1215–1249, Jan. 2018, https://doi.org/10.4236/jmp.2018.96073.
•    O. Ericok and J. Mason, Foundations of a Finite Non-Equilibrium Statistical Thermodynamics: Extrinsic Quantities. 2022.
•    U. Seifert, “First and Second Law of Thermodynamics at Strong Coupling,” Phys. Rev. Lett., vol. 116, no. 2, p. 020601, Jan. 2016, https://doi.org/10.1103/PhysRevLett.116.020601.
•    Y.-F. Chang, “Entropy Decrease in Isolated Systems: Theory, Fact and ‎Tests‎: Physics,” Int. J. Fundam. Phys. Sci., vol. 10, no. 2, Art. no. 2, Jun. 2020, https://doi.org/10.14331/ijfps.2020.330137.
•    H. Choi, “Size and Expansion of the Universe in Zero Energy Universe (Logical defenses for the Model ‘We are living in a black hole’ ),” Nov. 2016.
•    P. Halpern and N. Tomasello, “Size of the Observable Universe,” Adv. Astrophys., vol. 1, Nov. 2016, https://doi.org/10.22606/adap.2016.13001.
•    R. Hershkowitz et al., “Reasoning in Geometry,” in Perspectives on the Teaching of Geometry for the 21st Century: An ICMI Study, C. Mammana and V. Villani, Eds., in New ICMI Study Series. , Dordrecht: Springer Netherlands, 1998, pp. 29–83. https://doi.org/10.1007/978-94-011-5226-6_3.
•    “Euclid’s Elements, Book II, Proposition 10.” Accessed: Jun. 29, 2023. [Online]. Available: http://aleph0.clarku.edu/~djoyce/elements/bookII/propII10.html.
•    C. Masolo and L. Vieu, “Atomicity vs. Infinite Divisibility of Space,” in COSIT, 1999. https://doi.org/10.1007/3-540-48384-5_16.
•    N. Raos, “Atomism in greek philosophy,” Kem. U Ind. Chem. Chem. Eng., vol. 51, pp. 385–392, Jan. 2002.
•    S. W. Gaukroger, “Descartes’ Conception of Inference,” in Metaphysics and Philosophy of Science in the Seventeenth and Eighteenth Centuries: Essays in honour of Gerd Buchdahl, R. S. Woolhouse, Ed., in The Universityof Western Ontario Series in Philosophy of Science. , Dordrecht: Springer Netherlands, 1988, pp. 101–132. https://doi.org/10.1007/978-94-009-2997-5_6.
•    Heath, Thomas L, The Thirteen Books of Euclid’s Elements, translated from the text of Heiberg, with introduction and commentary, 2nd ed., vol. 3 vols. Cambridge (available in Dover reprint): University Press,1926.
•    N. F. Shul’ga, V. V. Syshchenko, A. I. Tarnovsky, V. I. Dronik, and A. Y. Isupov, “Regular and chaotic motion domains in the channeling electron’s phase space and mean level density for its transverse motionenergy,”J. Instrum., vol. 14, no. 12, pp. C12022–C12022, Dec. 2019, https://doi.org/10.1088/1748-0221/14/12/C12022.
•    B. T. Utelbayev, E. Suleimenov, and U. A.B., “Elementary Particles and Properties of Material Objects Review Article,” Dec. 2018.
•    S. Reucroft and E. Williams, “The Structure and Properties of Elementary Particles,” Oct. 2019.
•    R. Abreu and V. Guerra, “The concepts of work and heat and the first and second laws of thermodynamics,” Mar. 2012.
• S. Shahsavari and P. Torkaman, “Energy Conservation Principle from the Perspective of the Energy Structure Theory,” Asian J. Appl. Sci., vol. 10, no. 5, Nov. 2022, https://doi.org/10.24203/ajas.v10i5.6950.
• B. Xia, Z. Chen, C. Mi, and B. Robert, “External short circuit fault diagnosis for lithium-ion batteries,” in 2014 IEEE Transportation Electrification Conference and Expo (ITEC), Dearborn, MI: IEEE, Jun. 2014,pp. 1–7.https://doi.org/10.1109/ITEC.2014.6861806.
• Z. Chen, R. Xiong, J. Tian, X. Shang, and J. Lu, “Model-based fault diagnosis approach on external short circuit of lithium-ion battery used in electric vehicles,” Appl. Energy, vol. 184, pp. 365–374, Dec. 2016, https://doi.org/10.1016/j.apenergy.2016.10.026.
• A. Berizzi, A. Silvestri, D. Zaninelli, and S. Massucco, “Short-circuit current calculation: A comparison between methods of IEC and ANSI standards using dynamic simulation as reference,” IEEE Trans. Ind. Appl.Inst.Electr. Electron. Eng. U. S., vol. 30:4, https://doi.org/10.1109/IAS.1993.299168.
• F. V. Conte, P. Gollob, and H. Lacher, “Safety in the battery design: The short circuit,” World Electr. Veh. J., vol. 3, Dec. 2009, https://doi.org/10.3390/wevj3040719.
• M. F. Moad, “On Thevenin’s and Norton’s Equivalent Circuits,” IEEE Trans. Educ., vol. 25, no. 3, pp. 99–102, Aug. 1982, https://doi.org/10.1109/TE.1982.4321556.
• J. D. Enderle, “Thévenin’s and Norton’s Theorems,” in Bioinstrumentation, in Synthesis Lectures on Biomedical Engineering. , Cham: Springer International Publishing, 2006, pp. 53–61. https://doi.org/10.1007/978-3401616-5_6.
• R. V. Jensen, “Classical Chaos,” Am. Sci., vol. 75, no. 2, pp. 168–181, 1987.
• M. C. Gutzwiller, “Soft Chaos and the KAM Theorem,” in Chaos in Classical and Quantum Mechanics, M. C. Gutzwiller, Ed., in Interdisciplinary Applied Mathematics. , New York, NY: Springer, 1990, pp. 116–141. https://doi.org/10.1007/978-1-4612-0983-6_10.
• G. F. R. Ellis, U. Kirchner, and W. R. Stoeger, “Multiverses and physical cosmology,” Mon. Not. R. Astron. Soc., vol. 347, no. 3, pp. 921–936, Jan. 2004, https://doi.org/10.1111/j.1365-2966.2004.07261.x.
• J. Wisniak, “Conservation of Energy: Readings on the Origins of the First Law of Thermodynamics. Part I,” Educ. Quím., vol. 19, pp. 159–171, Jan. 2008, https://doi.org/10.22201/fq.18708404e.2008.2.25806