PHYSICS 361 (Classical Mechanics) Dr. Anatoli Frishman Web Page: 1

Introduction What is this course about A little bit of history –Galileo (1564 – 1642) –Newton (1642 – 1727) –Lagrange (1736 – 1813) –Hamilton (1805 – 1865) –Poincare (1854 – 1912) –Lyapunov (1857 – 1918) –Lorenz (1917 – 2008) Course organization Lectures Homework Exams (two midterm exams and a comprehensive final exam) Formula sheet Syllabus 2

1. Mechanics of material point Material point (point mass) – an object with an irrelevant dimension for the purposes of a particular problem. Position of material point in space: Cartesian coordinates: Velocity: Acceleration: Definitions 3

Newton’s laws Newton’s First Law (the low of Inertia) Existence of inertial systems of reference In inertial system of reference, any object acted by no net force remains at rest or continues its motion along straight line with constant velocity Newton’s Third Law Note: these two forces act on different objects. Never add these forces! Newton’s Second Law 4

5 Newton’s Second law as differential equation Example (constant force): Method 2: Method 1:

6 Example (Hook’s law): This is a second-order differential equation. The general solution contains two independents constants. Another form of the solution:

7 2. Polar and cylindrical coordinates A vector in polar and cylindrical coordinates coordinates: Polar: Cylindrical: Definitions: Some properties:

8 Derivatives in polar coordinates:

9 Kinetic energy in polar coordinates: Method 1: Method 2: Polar: Cylindrical:

10 Example (pendulum): mg L The same equation as for the Hook’s law