Browse: Keyword: Rigid Bodies

"Classical Mechanics: A Computational Approach, Fall 2008"

Abstract:: " We will study the fundamental principles of classical mechanics, with a modern emphasis on the qualitative structure of phase space. We will use computational ideas to formulate the principles of mechanics precisely. Expression in a computational framework encourages clear thinking and active exploration. We will consider the following topics: the Lagrangian formulation; action, variational principles, and equations of motion; Hamilton's principle; conserved quantities; rigid bodies and tops; Hamiltonian formulation and canonical equations; surfaces of section; chaos; canonical transformations and generating functions; Liouville's theorem and Poincaré integral invariants; Poincaré-Birkhoff and KAM theorems; invariant curves and cantori; nonlinear resonances; resonance overlap and transition to chaos; properties of chaotic motion. Ideas will be illustrated and supported with physical examples. We will make extensive use of computing to capture methods, for simulation, and for symbolic analysis."

Fundamentals of Physics

Abstract:: This course provides a thorough introduction to the principles and methods of physics for students who have good preparation in physics and mathematics. Emphasis is placed on problem solving and quantitative reasoning. This course covers Newtonian mechanics, special relativity, gravitation, thermodynamics, and waves.

Abstract:: Introduction to classical mechanics (see description under 8.01). Material is covered over a longer interval, so that the subject is completed by the end of the Independent Activities Period. During the first month of classes, substantial emphasis is given to reviewing and strengthening pre-calculus mathematics, basic physics concepts, and problem-solving skills. Delay in the use of calculus permits students more exposure to 18.01 before the material is used in the physics. Overall content, depth, and difficulty is otherwise identical to that of 8.01. Students receive credit for 8.01 on their transcripts. Credit cannot also be received for 8.012 or 8.01X.

Abstract:: Physics I is a first-year, first-semester course that provides an introduction to Classical Mechanics. It covers the basic concepts of Newtonian mechanics, fluid mechanics, and kinetic gas theory.

Abstract:: Introduces classical mechanics. Space and time: straight-line kinematics; motion in a plane; forces and equilibrium; experimental basis of Newton's laws; particle dynamics; universal gravitation; collisions and conservation laws; work and potential energy; vibrational motion; conservative forces; inertial forces and non-inertial frames; central force motions; rigid bodies and rotational dynamics.