Equations of motion of a structure under multidimensional seismic excitations

Equations of motion of a structure under multidimensional seismic excitations are established based on dynamics and kinematics. The seismic excitations considered include two translational components in horizontal and a rotational component about vertical. The dynamics of a structure under such excitations is much more profound than usual expectations sated by conventional theories; the new presented equations reveal the remarkable difference in the acceleration calculations of the super structure. As the dynamic equations are the underlying model of a structure that governing their dynamic properties, the new equations provide a ground stone for theoretical analyses and engineering applications. Restoring forces and damping forces are also presented in detail. And a control algorithm for the nonlinear structure is introduced by applying a sate space control approach.