Analytical Mechanics Course Outline and References
Explore the syllabus, course description, outline, and references for Analytical Mechanics covering topics like Newtonian mechanics, Lagrangian mechanics, Hamiltonian dynamics, and more. Dive deep into advanced mathematical concepts to understand the dynamics of particles and rigid bodies in various dimensions.
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Presentation Transcript
Analytical Mechanics Analytical Mechanics Syllabus / Course Description/ Course Outline/ References 1
Mechanics Lagrange& Hamilton Newton 2
Course Description Newtonian mechanics : is studied rigorously using advanced mathematical Topics treated include : dynamics, harmonic oscillations, central forces, *dynamics of rigid bodies Lagrangian, and Hamiltonian s Mechanics 3
Course Outline Course Outline Main Reference :Analytical Mechanics, Grant R. Fowles & George Cassiday 1. Introduction Vector algebra, coordinate systems, velocity and acceleration of a particle using curvilinear coordinate system. 2. Newtonian Mechanics in One Dimension Newton's laws and inertial systems. Simple applications of Newton ' s constant applied force. Position-dependent forces ( concept of potential energy) . Velocity- dependent force. (Ch. 2) 3. Oscillations, Linear restoring force: Harmonic motion. Damped harmonic motion. (Ch. 3), 4
Course Outline Course Outline 4. General Motion of a Particle in Three Dimensions General principles. Potential energy function in three-dimensional motion: The Del operator. Projectile motion. The harmonic oscillator in two and three dimensions. Motion of charged particles in electric and magnetic fields. Constrained motion of a particle. (Ch. 4) 5. Gravitation and Central Forces (Ch. 6) Kepler laws of planetary motion. Potential energy in a gravitational field. Energy equation of an orbit in a central field. Orbital energies in an inverse-square field. 5
Course Outline Course Outline 7. Lagrangian Mechanics (Ch. 10) Generalized coordinates. Lagrange's equations of motion for conservative systems. Generalized momenta. Generalized forces. Hamilton's equations and applications 6
Main References: Main References: 1. Analytical Mechanics. Grant R. Fowles & George L. Cassiday. Seventh Edition, Thomson, (2005). 2. Theory and Problems of Mechanics with an Introduction to Lagrange's equations and Hamiltonian theory, Murray R. Spiegel. McGraw-Hill company, (1980). 7
