Theoretical mechanics

Theoretical mechanics uses mathematical models to describe the motion and equilibrium of physical systems and their responses to forces.

Newton's laws of motion: Three laws relating a body's motion to inertia and the forces acting on it. They provide the force-based foundation for classical mechanical models.
Lagrangian mechanics: A formulation of classical mechanics based on kinetic and potential energy and the Euler–Lagrange equations. It derives motion using generalized coordinates and an energy function.
Rigid body dynamics: The study of the motion and forces of bodies treated as undeformable. It applies mechanical equations to translation and rotation together.
Isaac Newton: English mathematician and physicist who formulated the laws of motion and universal gravitation. His laws established the central force-based framework of classical mechanics.
Quantum mechanics: A physical theory describing matter and radiation through quantum states and probabilistic measurement outcomes. It replaces classical trajectories with quantum states at microscopic scales.
Principle of virtual work: A condition equating the virtual work of applied forces to zero for a system in equilibrium. It turns equilibrium into a condition on possible infinitesimal displacements.
Hamiltonian mechanics: A formulation of mechanics using coordinates, momenta, and a Hamiltonian function to describe time evolution. It recasts motion as evolution through phase space.
Analytical statics: The mathematical study of equilibrium using generalized coordinates and principles such as virtual work. It finds equilibrium without resolving every force into Cartesian components.
Joseph-Louis Lagrange: Mathematician and astronomer whose analytical methods reshaped mechanics in the eighteenth century. His Mécanique analytique organized mechanics around generalized coordinates and variational methods.
Special relativity: A theory of space, time, and motion in inertial frames, with the speed of light invariant. It modifies classical mechanics when speeds approach the speed of light.

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Applied mechanicsCompared with: It emphasizes general formulations, while applied mechanics targets concrete physical problems.