Classical Mechanics with Maple

Section 1.1: Introduction and Installation Instructions

Harald Kammerer
maple@jademountain.de

1.1.1 Introduction

Classical mechanics studies forces and their effects on bodies on a non-atomic scale. When these bodies are stationary, we talk about statics . When they are moving, we talk about kinetics. We speak of kinematics when we mean the motion of bodies caused by the action of forces. In some cases, only the geometry of the motion is of interest, regardless of the reason for the motion. To simplify the understanding of the following sections, we first define some fundamental terms. In the numerical examples of this course, we use these basic units by default.

Basic Units

The distance between two points in the space is mesured in units of 1 m (meter).

To define the position of a point in space we use a reference system. Usually this is described as a system of three orthogonal axes. A reference system which underlies Newtionian laws is called an inertial system . Every reference system which is moved relative to this inertial system by a uniform translation is also an inertial system. Measurements with respect to an inertial system are called absolute . On the earth, fixed reference systems are not real inertial systems, but the error is so small in practice that it can be neglected. So we can use the Newtonian laws on earth with adequate precision. Motions measured relative to the earth can be considered absolute .

time is measured in units of 1 s (second).

mass is mesured in units of 1 kg (kilogram)

f orce is deduced by the units of length, mass and time. The unit of the force is 1 N = 1 kg m / s^2 .

Organization of the Course

The course is organized as shown below. Each section contains enough material for several lectures.

Chapter 2: Kinematics of Mass Particles

section 2.1 Mass Particles in Cartesian, Polar and Natural Coordinates

section 2.2 Mass Particles in Relative Coordinates

Chapter 3: Kinetics of Mass Particles

section 3.1 Newton's Laws of Motion

section 3.2 Balance and Conservation of Energy

section 3.3 Linear Momentum

Chapter 4: Systems of Mass Particles and Rigid Bodies

section 4.1 Systems of Mass Particles

section 4.2 Systems of Plane Rigid Bodies

Chapter 5: Equations of Motion for Rigid Bodies and Systems of Rigid Bodies

section 5.1 The Analytic Method and the Lagrangian Equations

section 5.2 Worked Examples of the Synthetic and Analytic Methods

1.1.2 Installation Instructions for the Packages and Diagrams

In addition to the Maple worksheets, this course provides two Maple packages:

The dynamics package, which contains Maple 6 functions for performing basic computations in classical mechanics.

The figures package, which contains all of the Maple diagrams and animations used in the course. The figures were placed inside a package to avoid cluttering the exposition in the chapters with the Maple code used to generate the figures. The figures are provided in the form of Maple procedures, many of which take parameters, allowing the user to change their appearance interactively.

To install these packages:

1. Save the contents of the folders m6dynlib and m6dynfig in directories of your choosing, say C:/mylib/m6dynlib and C: / mylib / m6dynfig .

2. In any Maple worksheet where you want to use the package or view the figures, enter the commands:

> restart;

> libname:="C:/mylib/m6dynlib","C:/mylib/m6dynfig",libname;

> with(plots):with(plottools):with(linalg):

> with(dynamics);

> with(figures_chapter_2); #OR CHAPTER 3, OR 4 OR 5.