# Lectures onEngineering Mechanics

## Geometry and definitions in the textbook

A body occupies a region Ω in space. The position of an infinitesimal mass element dm of the body is defined by the position vector r, and the velocity of this mass element is v.

The momentum of a body Ω is defined as

GΩ vdm,
while the angular momentum with respect to an arbitrary point A is defined as
HAΩ r × vdm,

### Postulates

Euler's laws postulate that the motion of a body is governed by the force sum ΣF and the moment sum ΣMD with respect to a space-fixed point D acting on the body:

ΣF = dG/dt
ΣMD = dHD/dt.

## Pedagogical considerations

Although Statics, Particle dynamics and Rigid body dynamics emerge as special cases of Euler's laws for deformable bodies in general motion, it is the belief of the author that it would be a pedagogical mistake to start from the general theoretical framework in a first course of Engineering Mechanics. Introducing Statics first gives students a chance to develop theoretical skills in mathematical inference, vector algebra and the concept of the free-body diagram.

## Typesetting and graphics

• The typesetting is done with LaTeX using the Tufte-LaTeX document style, as inspired by Edward R. Tufte.
• The two-dimensional vector graphics are drawn using the XFig with LaTeX-interpreted mathematical content. Three-dimensional renderings are created from POV-Ray scripts with an XFig vector graphics overlay.
• Functional relations are plotted using Matplotlib in Python.
• The answers to almost all exersices are calculated by formulating the and solving the governing equations using the SymPy symbolic toolbox in Python.
Page responsible S. and E.-K. Lindström