Explore Lagrange multipliers and constraint forces in nonholonomic systems through a comprehensive lecture on analytical dynamics. Delve into the derivation of generalized constraint forces using d'Alembert's principle and their connection to Newtonian forces. Examine practical examples including a two-mass rigid rod system with a wheel constraint, a roller racer with pivoted masses, and a disk rolling down a hill. Investigate how different mass distributions affect the downhill racing performance of round rigid bodies, highlighting the crucial role of moment of inertia. Gain insights into advanced concepts in dynamics, constraint equations, and their applications in various mechanical systems.