Rigid body dynamics The result is a set of m equations of motion that define the dynamics of the rigid body system. If the generalized forces Q are derivable from a potential energy V(q...,q), then these equations of motion take the form In this case, introduce the Lagrangian, L=T-V, so these equations of motion become These are known as Lagrange's equations of motion. The linear and angular momentum of a rigid system of particles is formulated by measuring the position and velocity of the particles relative to the center of mass. Let the system of particles P, i=1...,n be located at the coordinates
Escape velocity In gravitational fields, "escape velocity" refers to the escape velocity of zero mass test particles relative to the barycenter of the masses generating the field. In most situations involving spacecraft the difference is negligible. For a mass equal to a Saturn V rocket, the escape velocity relative to the launch pad is 253.5 am/s (8 nanometers per year) faster than the escape velocity relative to the mutual center of mass. Ignoring all factors other than the gravitational force between the body and the object, an object projected vertically at speed formula_16 from the surface of a spherical body with escape