RZ Rui Zhang Academic portfolio
Menu
Back to reports archive

Research Reports

Lagrangian Mechanics and Variational Calculus

Jun 2025 · archived · UCL Year 1 Mathematics Project · Rui Zhang, Rebecca Withey

A rewritten LaTeX report based on a Year 1 summer mathematics department project about ordinary extrema, functionals, the Euler-Lagrange equation, shortest paths, the Beltrami identity, and the brachistochrone problem.

  • variational calculus
  • Lagrangian mechanics
  • Euler-Lagrange equation
Report PDFLaTeX source

Summary

This report reorganises a Year 1 summer mathematics department presentation into a written project note. It explains why ordinary calculus is sufficient for finite-dimensional equilibrium problems, then motivates variational calculus for problems where the unknown is an entire path or function.

Context

The original presentation covered a spring-mass example, functionals, the Euler-Lagrange equation, shortest paths, the brachistochrone problem, and the Beltrami identity. The public version is a generated LaTeX report intended to be easier to read and cite as portfolio material.

Notes on status

This is a project-report style artifact, not a peer-reviewed publication. It is included because it shows mathematical exposition, derivation, and early project development.