{"product_id":"lectures-on-mechanics-paperback-9780521428446","title":"Lectures on Mechanics (Paperback) 9780521428446","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eLectures on Mechanics\u003c\/font\u003e\u003cbr\u003e\r\n\r\n\r\n\u003c\/p\u003e\n\u003cp\u003e\u003cem\u003eBased on the 1991 LMS Invited Lectures given by Professor Marsden, this book discusses and applies symmetry methods to such areas as bifurcations and chaos in mechanical systems.\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"4\"\u003eJerrold E. Marsden (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9780521428446, Cambridge University Press\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003ePaperback, published 30 April 1992\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e268 pages\u003cbr\u003e22.9 x 15.2 x 1.5 cm, 0.4 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cem\u003e\u003cfont size=\"3\"\u003e\"...The virtue [of this book] is in the breadth, relevance, and complexity of the examples treated...\"   Mathematical Reviews\u003c\/font\u003e\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003eThe use of geometric methods in classical mechanics has proven to be a fruitful exercise, with the results being of wide application to physics and engineering. Here Professor Marsden concentrates on these geometric aspects, and especially on symmetry techniques. The main points he covers are: the stability of relative equilibria, which is analyzed using the block diagonalization technique; geometric phases, studied using the reduction and reconstruction technique; and bifurcation of relative equilibria and chaos in mechanical systems. A unifying theme for these points is provided by reduction theory, the associated mechanical connection and techniques from dynamical systems. These methods can be applied to many control and stabilization situations, and this is illustrated using rigid bodies with internal rotors, and the use of geometric phases in mechanical systems. To illustrate the above ideas and the power of geometric arguments, the author studies a variety of specific systems, including the double spherical pendulum and the classical rotating water molecule. This book, based on the 1991 LMS Invited Lectures, will be valued by pure and applied mathematicians, physicists and engineers who work in geometry, nonlinear dynamics, mechanics, and robotics.\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e1. Introduction\u003cbr\u003e 2. A crash course in geometric mechanics\u003cbr\u003e 3. Cotangent bundle reduction\u003cbr\u003e 4. Relative equilibria\u003cbr\u003e 5. The energy-momentum method\u003cbr\u003e 6. Geometric phases\u003cbr\u003e 7. Stabilization and control\u003cbr\u003e 8. Discrete reduction\u003cbr\u003e 9. Mechanical integrators\u003cbr\u003e 10. Hamiltonian bifurcations\u003cbr\u003e References.\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Mathematical modelling [\u003ca title=\"See our other books on Mathematical modelling\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Mathematical%20modelling%20%5BPBWH%5D%22\"\u003ePBWH\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"Cambridge University Press","offers":[{"title":"Default Title","offer_id":46007278436632,"sku":"9780521428446","price":56.78,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/products\/9780521428446i_f72acc3a-130b-4b00-884e-f2299621e622.jpg?v=1691381685","url":"https:\/\/freshlyprintedbooks.co.uk\/products\/lectures-on-mechanics-paperback-9780521428446","provider":"Freshly Printed Books","version":"1.0","type":"link"}