{"product_id":"perfect-form-9780691026633","title":"Perfect Form","description":"\u003cp\u003eWhat does the path taken by a ray of light share with the trajectory of a thrown baseball and the curve of a wheat stalk bending in the breeze? Each is the subject of a different study yet all are optimal shapes; light rays minimize travel time while a thrown baseball minimizes action. All natural curves and shapes  and many artificial ones  manifest such \"perfect form\" because physical principles can be expressed as a statement requiring some important physical quantity to be mathematically maximum  minimum  or stationary. Perfect Form introduces the basic \"variational\" principles of classical physics (least time  least potential energy  least action  and Hamiltons principle)  develops the mathematical language most suited to their application (the calculus of variations)  and presents applications from the physics usually encountered in introductory course sequences.  The text gradually unfolds the physics and mathematics. While other treatments postulate Hamiltons principle and deduce all results from it  Perfect Form begins with the most plausible and restricted variational principles and develops more powerful ones through generalization. One selection of text and problems even constitutes a non-calculus of variations introduction to variational methods  while the mathematics more generally employed extends only to solving simple ordinary differential equations. Perfect Form is designed to supplement existing classical mechanics texts and to present variational principles and methods to students who approach the subject for the first time.\u003c\/p\u003e","brand":"My Store","offers":[{"title":"Default Title","offer_id":45646866153525,"sku":"ByrdShop_0691026637","price":46.16,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0627\/8139\/0901\/files\/9780691026633.jpg?v=1781679312","url":"https:\/\/atxbooks.com\/products\/perfect-form-9780691026633","provider":"ATX Books","version":"1.0","type":"link"}