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Books on the topic 'Lagrange space'

Author: Grafiati
Published: 4 June 2025
Last updated: 6 July 2025

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1

Center, NASA Glenn Research, ed. Finite element simulation of a space shuttle solid rocket booster aft skirt splashdown using an arbitrary Lagrangian-Eulerian approach. NASA Glenn Research Center, 2003.

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2

Miron, Radu. The Geometry of Higher-Order Lagrange Spaces. Springer Netherlands, 1997. http://dx.doi.org/10.1007/978-94-017-3338-0.

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Miron, Radu, Dragos Hrimiuc, Hideo Shimada, and Sorin V. Sabau. The Geometry of Hamilton and Lagrange Spaces. Springer Netherlands, 2002. http://dx.doi.org/10.1007/0-306-47135-3.

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4

Radu, Miron, ed. The geometry of Hamilton and Lagrange spaces. Kluwer Academic Publishers, 2001.

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5

Brașov), National Seminar on Finsler and Lagrange Spaces (4th 1986 Universitatea din. The proceedings of the fourth National Seminar on Finsler and Lagrange Spaces. Universitatea din Brașov, 1986.

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6

National Seminar on Finsler and Lagrange Spaces (5th 1988 Brașov, Romania). The Proceedings of the Fifth National Seminar of Finsler and Lagrange Spaces: In honour of the 60th birthday of Professor Doctor, Radu Miron, Brașov, 10-15th of February 1988. Societatea de Stiinte Matematice din R.S. Romania, Universitatea din Brașov, 1989.

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7

Miron, Radu, and Mihai Anastasiei. The Geometry of Lagrange Spaces: Theory and Applications. Springer Netherlands, 1994. http://dx.doi.org/10.1007/978-94-011-0788-4.

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8

Munteanu, Gheorghe. Complex Spaces in Finsler, Lagrange and Hamilton Geometries. Springer Netherlands, 2004. http://dx.doi.org/10.1007/978-1-4020-2206-7.

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9

Miron, Radu. The Geometry of Lagrange Spaces: Theory and Applications. Springer Netherlands, 1994.

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10

Miron, Radu. The geometry of Lagrange spaces: Theory and applications. Kluwer Academic Publishers, 1994.

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11

Miron, Radu. Fibrate vectoriale, spații Lagrange, aplicații în teoria relativității. Editura Academiei Republicii Socialiste România, 1987.

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12

National Seminar on Finsler, Lagrange, and Hamilton Spaces (6th 1990 Brașov, Romania). The proceedings of the Sixth National Seminar on Finsler, Lagrange, and Hamilton Spaces. Edited by Atanasiu Gheorghe, Societatea de Științe Matematice din România., and Universitatea Transilvania. Societatea de Științe Matematice din România, 1992.

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13

Mihai, Anastasiei, and Antonelli Peter L, eds. Finsler and Lagrange geometries: Proceedings of a conference held on August 26-31 [2001 in] Iaşi, Romania. Kluwer Academic Publishers, 2003.

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14

Miron, Radu. The geometry of higher-order Lagrange spaces: Applications to mechanics and physics. Kluwer Academic, 1997.

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15

Key, Jay. How to Pick Up Women with a Drunk Space Ninja: The Adventures of Duke LaGrange, Book One. Star Wheel Books, 2018.

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16

Key, Jay. How to Pick Up Women with a Drunk Space Ninja: The Adventures of Duke LaGrange, Book One. Star Wheel Books, 2018.

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17

Finite element simulation of a space shuttle solid rocket booster aft skirt splashdown using an arbitrary Lagrangian-Eulerian approach. NASA Glenn Research Center, 2003.

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18

Coopersmith, Jennifer. Mathematics and physics preliminaries: of hills and plains and other things. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198743040.003.0003.

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The link between mathematics and physics is explained, and how the concepts “coordinates,” “generalized coordinates,” “time,” and “space” have evolved, starting with Galileo. It is also shown that “degrees of freedom” is a slippery but crucial idea. The important developments in “space research”, from Pythagoras to Riemann, are sketched. This is followed by the motivations for finding a flat region of “space”, and for Riemann’s invariant interval. A careful explanation of the three ways of taking an infinitesimal step (actual, virtual, and imperfect) is given. The programme of the Calculus of Variations is described and how this requires a virtual variation of a whole path, a path taken between fixed end-states. This then culminates in the Euler-Lagrange Equations or the Lagrange Equations of Motion. Along the way, the ideas virtual displacement and extremum are explained.
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19

Mann, Peter. Constrained Lagrangian Mechanics. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198822370.003.0008.

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This chapter builds on the previous two chapters to tackle constrained systems, using Lagrangian mechanics and constrained variations. The first section deals with holonomic constraint equations using Lagrange multipliers; these can be used to reduce the number of coordinates until a linearly independent minimal set is obtained that describes a constraint surface within configuration space, so that Lagrange equations can be set up and solved. Motion is understood to be confined to a constraint submanifold. The variational formulation of non-holonomic constraints is then discussed to derive the vakonomic formulation. These erroneous equations are then compared to the central Lagrange equation, and the precise nature of the variations used in each formulation is investigated. The vakonomic equations are then presented in their Suslov form (Suslov–vakonomic form) in an attempt to reconcile the two approaches. In addition, the structure of biological membranes is framed as a constrained optimisation problem.
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20

McDuff, Dusa, and Dietmar Salamon. From classical to modern. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198794899.003.0002.

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The first chapter develops the basic concepts of symplectic topology from the vantage point of classical mechanics. It starts with an introduction to the Euler–Lagrange equation and shows how the Legendre transformation leads to Hamilton’s equations, symplectic forms, symplectomorphisms, and the symplectic action. It ends with a brief overview of some modern results in the subject on the symplectic topology of Euclidean space, such as the Weinstein conjecture and the Gromov nonsqueezing theorem.
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21

(Editor), M. Anastasiei, and P. L. Antonelli (Editor), eds. Finsler and Lagrange Geometries (NATO Science). Springer, 2003.

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22

Deruelle, Nathalie, and Jean-Philippe Uzan. Hamiltonian mechanics. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198786399.003.0009.

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This chapter gives a brief overview of Hamiltonian mechanics. The complexity of the Newtonian equations of motion for N interacting bodies led to the development in the late 18th and early 19th centuries of a formalism that reduces these equations to first-order differential equations. This formalism is known as Hamiltonian mechanics. This chapter shows how, given a Lagrangian and having constructed the corresponding Hamiltonian, Hamilton’s equations amount to simply a rewriting of the Euler–Lagrange equations. The feature that makes the Hamiltonian formulation superior is that the dimension of the phase space is double that of the configuration space, so that in addition to point transformations, it is possible to perform more general transformations in order to simplify solving the equations of motion.
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23

Miron, R., Dragos Hrimiuc, Hideo Shimada, and Sorin V. Sabau. Geometry of Hamilton and Lagrange Spaces. Springer London, Limited, 2006.

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24

Geometry of Hamilton and Lagrange Spaces. Kluwer, 2002.

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25

Miron, R., Dragos Hrimiuc, Hideo Shimada, and Sorin V. Sabau. The Geometry of Hamilton and Lagrange Spaces (Fundamental Theories of Physics, Volume 118) (Fundamental Theories of Physics). Springer, 2001.

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26

Coopersmith, Jennifer. Lagrangian Mechanics. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198743040.003.0006.

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It is demonstrated how d’Alembert’s Principle can be used as the basis for a more general mechanics – Lagrangian Mechanics. How this leads to Hamilton’s Principle (the Principle of Least Action) is shown mathematically and in words. It is further explained why Lagrangian Mechanics is so general, why forces of constraint may be ignored, and how external conditions lead to “curved space.” Also, it is explained why the Lagrangian, L, has the form L = T − V (where T is the kinetic energy and V is the potential energy), and why T is in “quadratic form” (T = 1/2mv2). It is shown how Noether’s Theorem leads to a more fundamental definition of energy and links the conservation of energy to the homogeneity of time. The ingenious Lagrange multipliers are explained, and also generalized forces and generalized coordinates.
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27

Mann, Peter. Point Transformations in Lagrangian Mechanics. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198822370.003.0009.

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This chapter discusses point transformations in Lagrangian mechanics. Sometimes, when solving problems, it is useful to change coordinates in velocity phase space to better suit and simplify the system at hand; this is a requirement of any physical theory. This change is often motivated by some experimentally observed physicality of the system or may highlight new conserved quantities that might have been overlooked using the old description. In the Newtonian formalism, it was a bit of a hassle to change coordinates and the equations of motion will look quite different. In this chapter, point transformations in Lagrangian mechanics are developed and the Euler–Lagrange equation is found to be covariant. The chapter discusses coordinate transformations, parametrisation invariance and the Jacobian of the transform. Re-parametrisations are also included.
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28

Munteanu, Gheorghe. Complex Spaces in Finsler, Lagrange and Hamilton Geometries. Springer, 2010.

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29

Complex spaces in Finsler, Lagrange, and Hamilton geometries. Kluwer Academic Publishers, 2004.

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30

Munteanu, Gheorghe. Complex Spaces in Finsler, Lagrange and Hamilton Geometries. Springer London, Limited, 2004.

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31

Munteanu, Gheorghe. Complex Spaces in Finsler, Lagrange and Hamilton Geometries. Springer, 2014.

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32

Miron, R., and P. L. Antonelli. Lagrange and Finsler Geometry: Applications to Physics and Biology. Springer, 2013.

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33

Miron, R., and P. L. Antonelli. Lagrange and Finsler Geometry: Applications to Physics and Biology. Springer, 2010.

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34

Antonelli, P. L., and Mihai Anastasiei. Finsler and Lagrange Geometries: Proceedings of a Conference Held on August 26-31, Iaşi, Romania. Springer, 2013.

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35

Coopersmith, Jennifer. The Lazy Universe. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198743040.001.0001.

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Action and the Principle of Least Action are explained: what Action is, why the Principle of Least Action works, why it underlies all physics, and what are the insights gained into energy, space, and time. The physical and mathematical origins of the Lagrange Equations, Hamilton’s Equations, the Lagrangian, the Hamiltonian, and the Hamilton-Jacobi Equation are shown. Also, worked examples in Lagrangian and Hamiltonian Mechanics are given. However the aim is to explain physics rather than to give a technical mastery of the subject. Therefore, much of the mathematics is in the appendices. While there is still some mathematics in the main text, the reader may select whether to work through, skim-read, or skip over it: the “story-line” will just about be maintained whatever route is chosen. The work is a much-reduced and simplified version of the outstanding text, “The Variational Principles of Mechanics” written by Cornelius Lanczos in 1949. That work is barely known today, and the present work may be considered as a tiny stepping-stone toward it. A principle that underlies all of physics will have wider repercussions; it is also to be appreciated in an aesthetic sense. It is hoped that this book will lead the reader to the widest possible understanding of the Principle of Least Action. Ideas such as Variational Mechanics, phase space, Fermat’s Principle, and Noether’s Theorem are explained.
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36

Miron, R., Dragos Hrimiuc, Hideo Shimada, and Sorin V. Sabau. The Geometry of Hamilton and Lagrange Spaces (Fundamental Theories of Physics). Springer, 2001.

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37

Miron, R. Geometry of Higher-Order Lagrange Spaces: Applications to Mechanics and Physics. Springer, 2013.

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38

Miron, R. The Geometry of Higher-Order Lagrange Spaces: Applications to Mechanics and Physics. Springer, 2014.

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39

The Geometry of Higher-Order Lagrange Spaces: Applications to Mechanics and Physics. Springer, 2010.

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40

Dufour, Jean-Paul, and Nguyen Tien Zung. Poisson Structures and Their Normal Forms. Springer London, Limited, 2006.

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41

T. Michaltsos, George, and Ioannis G. Raftoyiannis, eds. Bridges’ Dynamics. BENTHAM SCIENCE PUBLISHERS, 2012. http://dx.doi.org/10.2174/97816080522021120101.

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Bridges’ Dynamics covers the historical review of research and introductory mathematical concepts related to the structural dynamics of bridges. The e-book explains the theory behind engineering aspects such as 1) dynamic loadings, 2) mathematical concepts (calculus elements of variations, the d’ Alembert principle, Lagrange’s equation, the Hamilton principle, the equations of Heilig, and the δ and H functions), 3) moving loads, 4) bridge support mechanics (one, two and three span beams), 5) Static systems under dynamic loading 6) aero-elasticity, 7) space problems (2D and 3D) and 8) absorb systems (equations governing the behavior of the bridge-absorber system). The e-book is a useful introductory textbook for civil engineers interested in the theory of bridge structures.
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