In this study, the kinetic energy equation is firstly derived from the basic equation in the rotating coordinate system, and then the energy functional describing the change rate of tropical cyclone (TC) intensity is defined by the local change rate of kinetic energy. Afterwards, the Euler-Lagrange equation is obtained by taking the variation of the functional. The equation shows that when the change rate of TC intensity reaches the maximum, the friction, the pressure gradient force, the gravity and the gradient of kinetic energy are balanced. Therefore, the vector determined by these four forces in the balance equation can be used as a predictor of TC intensity, which can more accurately determine the time when the intensity change rate of TCs reaches the maximum. Furthermore, the maximum vortex in a rotational field is extracted by the variational decomposition of wind field, and the analytical solution of vorticity and flow field are obtained when TC intensity changes the fastest. The conclusion has certain practical value for studying the variation trend of velocity and the spatial structure of TC in the evolution of TC, and provides certain theoretical guidance for TC track and intensity forecast.