The study of mechanics is the cornerstone of classical and applied physics. Described as the "motion of bodies under the action of forces", the contemporary understanding of mechanics enables both theoretical breakthroughs and advances in robotics, industrial systems, aerospace systems, and an innumerable collection of other applications (Goodstein).
Here, I attempt to summarize the contemporary view of mechanics, with a uniquely "modern" flavor focused towards ongoing research in robotics, scientific computing, numerical methods, and optimization.
The Principle of Stationary Action (PSA) provides the foundation for much of contemporary mechanics applications. Rather than attempting to replace Newton's work, it elevates his contributions by providing an elegant formulation for classical mechanics.
Principle of Stationary Action
Goodstein, David L. "Mechanics". Encyclopaedia Britannica. https://www.britannica.com/science/mechanics (accessed August 4, 2026)