The dynamics of a particle, moving in background electromagnetic and gravitational fields, is revisited from a Lie group cohomological perspective. Physical constants characterising the particle appear as central extension parameters of a group which is obtained from a previously extended kinematical group (Poincare or Galilei) by making local some subgroup. The corresponding dynamics is generated by a vector field inside the kernel of a presymplectic form, which is derived from the canonical left-invariant one-form on the extended group. The nonrelativistic (Newtonian) limit is derived from the geodesic motion via an Inonu-Wigner contraction. A deeper analysis of the cohomological structure reveals the possibility of a new force associated with a nontrivial mixing of gravity and electromagnetism leading to testable predictions, such as a mass difference between charged particles and antiparticles.