Preliminaries

Every subject rests on a set of choices about how to think before any real work begins. In mechanics, the most consequential choice is the language we use to describe physical reality. This book adopts a vector-first approach: forces, positions, velocities and accelerations are vectors from the outset, expressed in component form relative to explicit coordinate systems. We never reduce a three-dimensional problem to a collection of ad-hoc scalar equations and angle sketches; instead, we write the vector relations directly and let the algebra follow.

The second choice concerns computation. Rather than solving equations by hand and reserving the computer for verification, we treat symbolic and numerical computation as integral parts of the modelling process. Python, together with SymPy for symbolic mathematics and NumPy for numerical work, serves as our computational workbench throughout the book. This combination lets us solve systems of equations exactly when possible, integrate differential equations numerically when necessary, and visualize results immediately.

We begin by establishing the vector notation and conventions that every subsequent chapter relies on, then work through a concrete example to see how vectors and code come together in practice. The remaining chapters introduce the computational tools themselves: a practical guide to SymPy, NumPy and Matplotlib, installation instructions for Python, and a broader discussion of why computer-supported mechanics deserves to be taken seriously as a pedagogical and engineering methodology.