Matches in SemOpenAlex for { <https://semopenalex.org/work/W4249733197> ?p ?o ?g. }
Showing items 1 to 72 of
72
with 100 items per page.
- W4249733197 abstract "Abstract This book begins with the ancient parts of classical mechanics: the variational principle, Lagrangian and Hamiltonian formalisms, and Poisson brackets. The simple pendulum provides a glimpse of the beauty of elliptic curves, which will also appear later in rigid body mechanics. Geodesics in Riemannian geometry are presented as an example of a Hamiltonian system. Conversely, the path of a non-relativistic particle is a geodesic in a metric that depends on the potential. Orbits around a black hole are found. Hamilton-Jacobi theory is discussed, showing a path towards quantum mechanics and a connection to the eikonal of optics. The three body problem is studied in detail, including small orbits around the Lagrange points. The dynamics of a charged particle in a magnetic field, especially a magnetic monopole, is studied in the Hamiltonian formalism. Spin is shown to be a classical phenomenon. Symplectic integrators that allow numerical solutions of mechanical systems are derived. A simplified version of Feigenbaum's theory of period doubling introduces chaos. Following a classification of Mobius transformations, this book studies chaos on the complex plane: Julia sets, Fatou sets, and the Mandelblot are explained. Newton's method for solution of non-linear equations is viewed as a dynamical system, allowing a novel approach to the reduction of matrices to canonical form. This is used as a stepping stone to the KAM theory of maps of a circle to itself, unravelling a connection to the Diophantine problem of number theory. KAM theory of the solution of the Hamilton-Jacobi equation using Newton's iteration concludes the book." @default.
- W4249733197 created "2022-05-12" @default.
- W4249733197 creator A5086028741 @default.
- W4249733197 date "2013-07-25" @default.
- W4249733197 modified "2023-10-16" @default.
- W4249733197 title "Advanced Mechanics" @default.
- W4249733197 doi "https://doi.org/10.1093/acprof:oso/9780199670857.001.0001" @default.
- W4249733197 hasPublicationYear "2013" @default.
- W4249733197 type Work @default.
- W4249733197 citedByCount "4" @default.
- W4249733197 countsByYear W42497331972019 @default.
- W4249733197 countsByYear W42497331972020 @default.
- W4249733197 crossrefType "monograph" @default.
- W4249733197 hasAuthorship W4249733197A5086028741 @default.
- W4249733197 hasConcept C109798219 @default.
- W4249733197 hasConcept C121332964 @default.
- W4249733197 hasConcept C121770821 @default.
- W4249733197 hasConcept C134306372 @default.
- W4249733197 hasConcept C136864674 @default.
- W4249733197 hasConcept C140279962 @default.
- W4249733197 hasConcept C151342819 @default.
- W4249733197 hasConcept C15184713 @default.
- W4249733197 hasConcept C165818556 @default.
- W4249733197 hasConcept C188845816 @default.
- W4249733197 hasConcept C202444582 @default.
- W4249733197 hasConcept C206183056 @default.
- W4249733197 hasConcept C206444204 @default.
- W4249733197 hasConcept C2778860007 @default.
- W4249733197 hasConcept C33923547 @default.
- W4249733197 hasConcept C37914503 @default.
- W4249733197 hasConcept C499771625 @default.
- W4249733197 hasConcept C51568863 @default.
- W4249733197 hasConcept C62520636 @default.
- W4249733197 hasConcept C74650414 @default.
- W4249733197 hasConcept C84114770 @default.
- W4249733197 hasConceptScore W4249733197C109798219 @default.
- W4249733197 hasConceptScore W4249733197C121332964 @default.
- W4249733197 hasConceptScore W4249733197C121770821 @default.
- W4249733197 hasConceptScore W4249733197C134306372 @default.
- W4249733197 hasConceptScore W4249733197C136864674 @default.
- W4249733197 hasConceptScore W4249733197C140279962 @default.
- W4249733197 hasConceptScore W4249733197C151342819 @default.
- W4249733197 hasConceptScore W4249733197C15184713 @default.
- W4249733197 hasConceptScore W4249733197C165818556 @default.
- W4249733197 hasConceptScore W4249733197C188845816 @default.
- W4249733197 hasConceptScore W4249733197C202444582 @default.
- W4249733197 hasConceptScore W4249733197C206183056 @default.
- W4249733197 hasConceptScore W4249733197C206444204 @default.
- W4249733197 hasConceptScore W4249733197C2778860007 @default.
- W4249733197 hasConceptScore W4249733197C33923547 @default.
- W4249733197 hasConceptScore W4249733197C37914503 @default.
- W4249733197 hasConceptScore W4249733197C499771625 @default.
- W4249733197 hasConceptScore W4249733197C51568863 @default.
- W4249733197 hasConceptScore W4249733197C62520636 @default.
- W4249733197 hasConceptScore W4249733197C74650414 @default.
- W4249733197 hasConceptScore W4249733197C84114770 @default.
- W4249733197 hasLocation W42497331971 @default.
- W4249733197 hasOpenAccess W4249733197 @default.
- W4249733197 hasPrimaryLocation W42497331971 @default.
- W4249733197 hasRelatedWork W1487433996 @default.
- W4249733197 hasRelatedWork W1557187315 @default.
- W4249733197 hasRelatedWork W1583319952 @default.
- W4249733197 hasRelatedWork W1969056347 @default.
- W4249733197 hasRelatedWork W2027225009 @default.
- W4249733197 hasRelatedWork W2804174466 @default.
- W4249733197 hasRelatedWork W3013347551 @default.
- W4249733197 hasRelatedWork W3022518536 @default.
- W4249733197 hasRelatedWork W4214906288 @default.
- W4249733197 hasRelatedWork W4252852927 @default.
- W4249733197 isParatext "false" @default.
- W4249733197 isRetracted "false" @default.
- W4249733197 workType "book" @default.