Analytical mechanics. ([2016])

• Record Type: Book
• Further Information: Note: Carl S. Helrich.
• Authors: Helrich, Carl S
• Contents: Intro; Preface; Contents; 1 History; 1.1 Introduction; 1.2 Ancient Greece; 1.2.1 Milesians; 1.2.2 Beyond Miletus; 1.2.3 Atomism; 1.2.4 Plato; 1.2.5 Aristotle; 1.2.6 Reflection on Greek Science; 1.3 Islamic Science; 1.3.1 The Rise of Islamic Science; 1.3.2 Expansion and Contact; 1.3.3 Islam and Greek Astronomy; 1.3.4 Islamic Astronomy; 1.3.5 Decline of Islamic Science; 1.3.6 Reflection on Islamic Science; 1.4 Europe Encounters Islamic Science; 1.5 Medieval Physics; 1.6 European Scientific Revolution; 1.7 Newton; 1.7.1 Introduction; 1.7.2 The Person; 1.7.3 Disputes; 1.7.4 Principia 1.7.5 Newtonian Concepts1.8 Eighteenth Century; 1.8.1 Maupertuis; 1.8.2 Euler; 1.8.3 Lagrange; 1.9 Hamilton and Jacobi; 1.9.1 Hamilton's Goal; 1.9.2 The First Essay; 1.9.3 The Second Essay; 1.10 Jacobi; 1.10.1 Jacobi 1837a; 1.10.2 Jacobi 1837b; 1.11 Summary; 1.12 Questions; 2 Lagrangian Mechanics; 2.1 Introduction; 2.2 Kinematics; 2.2.1 Rectangular Cartesian; 2.2.2 Cylindrical; 2.2.3 Spherical; 2.3 From Newton's Laws; 2.3.1 General Formulation; 2.3.2 Generalized Coordinates; 2.3.3 Virtual Displacement; 2.3.4 D'Alembert's Principle; 2.3.5 Euler -- Lagrange Equations; 2.4 Variational Calculus 2.4.1 Functionals2.4.2 Extrema of Functionals; 2.4.3 Euler Problem; 2.4.4 Hamilton's Principle; 2.5 Constraints; 2.5.1 Rolling; 2.5.2 Holonomic and Nonholonomic Constraints; 2.5.3 Lagrange Undetermined Multipliers; 2.5.4 Forces of Constraint; 2.6 Cyclic Coordinates; 2.7 Summary; 2.8 Exercises; 3 Hamiltonian Mechanics; 3.1 Introduction; 3.2 Legendre Transformation; 3.3 The Hamiltonian; 3.4 The Canonical Equations; 3.5 Constraints; 3.6 Rutherford Scattering; 3.7 Summary; 3.8 Exercises; 4 Solid Bodies; 4.1 Introduction; 4.2 The Vector Space; 4.2.1 Dirac Vectors; 4.2.2 Scalar Product 4.2.3 Representation4.3 Einstein Sum Convention; 4.4 Kinematics; 4.4.1 Reference Frames; 4.4.2 Rotation of the Basis; 4.4.3 Combined Velocities; 4.4.4 General Rolling Constraint; 4.5 Rigid Body Dynamics; 4.5.1 General Kinetic Energy; 4.5.2 Inertia Tensor; 4.5.3 Rotational Potential Energy; 4.5.4 Rotational Canonical Equations; 4.6 Summary; 4.7 Exercises; 5 Hamilton -- Jacobi Approach; 5.1 Introduction; 5.2 Hamilton's Idea; 5.3 Jacobi's Contribution; 5.4 Time Dependence; 5.5 Hamilton -- Jacobi Equation; 5.6 Canonical Transformation; 5.6.1 The Generating Function; 5.6.2 Conservative Systems 5.6.3 Time Dependent Hamiltonian5.6.4 Separation of Variables; 5.7 Action and Angle Variables; 5.8 Poisson Brackets; 5.9 And the Quantum Theory; 5.9.1 Heisenberg Indeterminacy; 5.9.2 The Schrödinger Equation; 5.10 Summary; 5.11 Exercises; 6 Complex Systems; 6.1 Introduction; 6.2 Integrable Systems; 6.3 The Hénon -- Heiles System; 6.3.1 Integrals of the Motion; 6.3.2 Equations of Motion; 6.3.3 Trajectories; 6.3.4 Poincaré Sections; 6.4 Summary; 7 Chaos in Dynamical Systems; 7.1 Introduction; 7.2 The Rössler System; 7.2.1 Rössler Equations; 7.2.2 Numerical Solution; 7.2.3 Rössler Attractor I
• Publisher Details: Cham, Switzerland : Springer
• Publication Date: 2016
• Copyright Date: 2017
• Extent: 1 online resource (xv, 349 pages), illustrations
• Subjects: 531.01/515; Physics; Mechanics, Analytic; Mechanics, Analytic; Science -- Mathematical Physics; Technology & Engineering -- Mechanical; Mathematical physics; Mechanics of solids; Mechanics; Mathematical physics; Mechanics, applied; Science -- Mechanics -- General; Classical mechanics; Electronic books
• Languages: English
• ISBNs: 9783319444918; 3319444913
• Related ISBNs: 9783319444901
• Notes: Note: Includes bibliographical references and index.; Note: Online resource; title from PDF title page (SpringerLink, viewed October 11, 2016).
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.