PH3110 Theoretical Mechanics I ... (3-0-0) f ... 3 Cr

An intermediate study of mechanics including the study of relativistic mechanics, kinematics, Newtonian mechanics of a single particle, oscillations, motion in non-inertial reference frames, and gravitation and central-force motion.

Prerequisites: PH2400 and MA3530 (Intro. Diff. Equations)

This course is a prerequisite for PH3111 and PH4210.

Texts (Fall, 2004):

• Analytical Mechanics, 7 ^th Edition, Fowles and Cassiday (ISBN 0-534-49492-7)
• Mathematical Handbook of Formulas & Tables, 2 ^nd Edition, Spiegel & Liu (ISBN 0-07-038203-4)

• Analytical Mechanics, 6 ^th Edition, Fowles and Cassiday (ISBN 0-03-022317-2)

Analytical Mechanics, 5^th Edition, Fowles and Cassiday
Basic Concepts in Relativity and Early Quantum Theory, Resnick and Halliday
Classical Dynamics of Particles and Systems, 3^rd edition, Marion and Thornton

Typical Topics (# of Lectures)

• The Galilean Transformation
• Einstein's Postulates
• The Lorentz Transformation and Relativistic Kinematics
• Relativistic Dynamics

• Vectors
• Vector Algebra: Addition, Scalar Multiplication, Subtraction, Scalar Product, Vector Product, Triple Product
• Vector Calculus: Derivatives of Vectors, Derivatives of Products, Vector Integration
• Kinematics
• Position, Velocity and Acceleration: Cartesian Coordinates
• Tangential and Normal Components of Acceleration
• Velocity and Acceleration in Some Orthogonal Curvilinear Coordinate Systems

3. Newtonian Mechanics: Rectilinear Motion of a Single Particle (5)

• Newton's Laws of Motion
• Constant Forces
• Time-Dependent Forces
• Velocity-Dependent Forces
• Position-Dependent Forces: Kinetic and Potential Energies

4. Oscillations (5)

• Linear Restoring Force: Harmonic Motion
• The Damped Harmonic Oscillator
• Forced Harmonic Motion: Resonance

5. Particle Motion in Three Dimensions (6)

• Auxiliary Principles of Newtonian Dynamics
• Torque and Angular Momentum
• Work and Kinetic Energy
• Conservative Forces and Potential Energy
• Separable Forces: Projectile Motion
• The Harmonic Oscillator in Two and Three Dimensions
• The Simple Pendulum

6. Non-inertial Reference Frames (6)

• Translation of the Coordinate System and Inertial Frames
• Rotating Coordinate Systems
• Dynamics in an Accelerating Reference Frame
• Motion Relative to the Earth
• Static Effects
• Dynamic Effects: Projectile Motion
• Foucault's Pendulum

7. Central Forces and Celestial Mechanics (8)

• Newton's Universal Law of Gravitation
• Gravitational Field and Gravitational Potential
• Motion under a Central Force
• Kepler's Second Law
• Energy and the Equation of Motion
• Inverse Square Force Law
• Orbital Energies and Classification of Orbits
• Kepler's First Law
• Kepler's Third Law

Total Number of Lectures: 41

Course Rationale:
The first course of two at the intermediate level in mechanics, one of the well-established core areas of Physics. It provides an in-depth study of mechanics at a higher level of mathematical skill than in the introductory course and covers material considered essential for an undergraduate physics major and closely related majors. It is a required course for all SPH and SAP majors.