On the motion of particles and strings, presymplectic mechanics, and the variational bicomplex

Examples of equations of motion in classical relativistic mechanics are studied: the equations of motion of a charged spinning particle moving in a space-time (with or without torsion) in the presence of an electromagnetic field are derived via Souriau presymplectic reduction. Then, the extension of Souriau's ideas to Lagrangian field theory due to Witten, Crnković, Zuckerman is reviewed using the variational bicomplex, the basic properties of the Lund Regge equations describing the motion of a string interacting with a scalar field and moving in Minkowski spacetime are recalled, and a symplectic structure for their space of solutions is found.