03636nam a22004575i 4500001001800000003000900018005001700027007001500044008004100059020001800100024003500118050001700153050001200170072001600182072002300198072001500221100008600236245015800322250001800480264006900498300006300567336002600630337002600656338003600682347002400718505018700742520186400929650001502793650002602808650002102834650002502855650003702880650002602917650002102943710003402964773002602998776003603024776003603060776003603096856004603132978-3-031-55202-1DE-He21320251030112043.0cr nn 008mamaa240515s2024    sz |    s    |||| 0|eng d  a97830315520217 a10.1007/978-3-031-55202-12doi 4aQC120-168.85 4aQA808.2 7aPHD2bicssc 7aSCI0410002bisacsh 7aPHD2thema1 aMohallem, José Rachid.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut10aLagrangian and Hamiltonian Mechanicsh[electronic resource] :bA Modern Approach with Core Principles and Underlying Topics /cby José Rachid Mohallem.  a1st ed. 2024. 1aCham :bSpringer Nature Switzerland :bImprint: Springer,c2024.  aXI, 142 p. 23 illus., 2 illus. in color.bonline resource.  atextbtxt2rdacontent  acomputerbc2rdamedia  aonline resourcebcr2rdacarrier  atext filebPDF2rda0 aChapter 1: Fundamentals -- Chapter 2: Lagrangian mechanics with L = T – V -- Chapter 3: Hamiltonian mechanics -- Chapter 4: Lagrangian and Hamiltonian introduction of field theory.  aThis book serves as a textbook for an analytical mechanics course, a fundamental subject of physics, that pays special attention to important topics that are not discussed in most standard textbooks. Readers are provided with a clear understanding of topics that are usually inaccessible to the undergraduate level and that are critical to learning Lagrangian and Hamiltonian mechanics. Each chapter also includes worked problems and solutions, as well as additional exercises for readers to try. This book begins with the fundamentals of analytical mechanics, concisely introducing readers to the calculus of variations, Hamilton’s Principle, and Lagrange’s equations. While presenting readers with these core topics, the author uses an intuitive approach to delve into essential questions, such as where Galilean invariance lies in Lagrangian mechanics and how Hamilton’s Principle of Least Action encompasses Newton’s three laws, interesting conclusions that often go unnoticed. In fact, Hamilton’s principle is taken throughout as the very origin of classical physical laws, and the choice of appropriate Lagrangians in each case as the real theoretical challenge, meaning that forms of Lagrangian which differ from the standard one are not mere curiosities but, instead, the general rule. This book clarifies common misunderstandings that students face when learning the subject and formally rationalizes concepts that are often difficult to grasp. In addition, the final chapter provides an introduction to a Lagrangian field theory for those interested in learning more advanced topics. Ideal for upper undergraduate and graduate students, this book seeks to teach the intrinsic meaning of the principles and equations taught in an analytical mechanics course and convey their usefulness as powerful theoretical instruments of modern physics. 0aMechanics. 0aMathematical physics. 0aOperator theory.14aClassical Mechanics.24aMathematical Methods in Physics.24aMathematical Physics.24aOperator Theory.2 aSpringerLink (Online service)0 tSpringer Nature eBook08iPrinted edition:z978303155201408iPrinted edition:z978303155203808iPrinted edition:z978303155204540uhttps://doi.org/10.1007/978-3-031-55202-1