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
Brain-to-body mass ratio Brain-to-body mass ratio Brain-to-body mass ratio, also known as the brain-to-body weight ratio, is the ratio of brain mass to body mass, which is hypothesized to be a rough estimate of the intelligence of an animal, although fairly inaccurate in many cases. A more complex measurement, encephalization quotient, takes into account allometric effects of widely divergent body sizes across several taxa. The raw brain-to-body mass ratio is however simpler to come by, and is still a useful tool for comparing encephalization within species or between fairly closely related species. Brain size usually increases with body size in animals (i.e. large