spaces e equipped euclidean structure euclidean structure defined kinetic energy single multidimensional particle unit mass math displaystyle math equal sum kinetic energies three dimensional particles masses math displaystyle ldots n math numblk math frac vert mathbf v vert sum n frac vert mathbf v vert math constraints internal coordinates cases motion particles masses math displaystyle ldots n math constrained typical constraints look like scalar equations form constraints form called holonomic scleronomic terms radius vector math displaystyle mathbf
Natural science Physics Newtonian dynamics