Intuitive Concept or Physical Meaning of Lagrangian
- 1 Department of Biofunctional and Mechanical Systems, Institute of Industrial Science, The University of Tokyo, Tokyo, Japan
Abstract
The authors have been studying on the principle of motion generation behind animals, mainly human, and have reached a certain milestone with it in [1]. Because [1] ended up being very interdisciplinary, the author has been looking for an opportunity to close in on the part where we have grasped the conceptual idea of a Lagrangian. This paper proposes the physical meaning or its intuitive concept of a Lagrangian. This is a daring attempt because the topic is over 240 years of enigma, whereby so many have neglected of its absence, and physics has gone further towards its frontiers of their time, and has successfully flourished. Meanwhile, Lagrangian is not getting enough of teachers’ attention on students getting stuck on this function, despite the fact that it is a strong foundation as is only the beginning towards Hamiltonian formalism, general relativity, and modern physics of today. This paper’s sole motive is to answer what the title says in detail, helping each and everyone who faces Lagrangian for their first time. The paper is positioned to be a supplement for [1]. This literature had three topics bound into one. Out of the three, this document focuses in the part of the intuitive meaning of Lagrangian, since the paper had contents related to multiple disciplines. The author finds it worthy to discuss this topic in an independent, more detailed manner.
- Morita, S. (2012) Trajectory Generation between Two Arbitrary States Based on Hamilton’s Principle—A Variable Substitution Method. International Journal of Humanoid Robotics, 9, 3. http://www.worldscientific.com/doi/pdf/10.1142/So219843612500235 http://dx.doi.org/10.1142/S0219843612500235
- Lifshitz, E.M. and Landau, L.D. (1981) Mechanics. 3rd Edition, Vol. 1, Butterworth-Heinmann, Oxford.
- Arnold, V.I. (1997) Mathematical Methods of Classical Mechanics. 2nd Edition, Springer, New York.
- Goldstein, H., Poole, C.P. and Safko, J.L. (2013) Classical Mechanics. 3rd Edition, Pearson Education Limited, Essex.
- Lanczos, C. (1986) The Variational Principles of Mechanics. 4th Edition, Dover, New York.
- Suto, Y. (2008) Analytical Mechanics Quantum Theory. University of Tokyo Press, Tokyo. (In Japanese)
- Cruiel, E. (2014) Classical Mechanics Is Lagrangian; It Is Not Hamiltonian. British Journal for the Philosophy of Science, 65, 269-321. http://www.bjps.oxfordjournals.org/content/early/2013/05/11/bjps.axs034.abstract http://dx.doi.org/10.1093/bjps/axs034