This book focuses on analytically approximate methods in the nonlinear dynamics of rigid bodies with cavities partially filled with liquid. Utilizing the Bateman-Luke variational formalism and perturbation theory, it presents approximate equations for the spatial motions of the body-liquid system, formulated as a finite-dimensional system of nonlinear ordinary differential equations. These equations couple the quasi-velocities of the rigid body with generalized coordinates that represent the natural sloshing modes. The text proposes algorithms for calculating hydrodynamic coefficients within the mathematical models, providing numerical values for various tank shapes and liquid fillings. Additionally, it derives models for contained liquids exhibiting Newton-type dissipation, along with formulas for hydrodynamic force and moment based on solid body quasi-velocities and sloshing-related coordinates. The book classifies steady-state sloshing regimes for harmonic excitations of upright circular and conical tanks, comparing theoretical results with existing experimental data. It serves as a valuable resource for both experienced and novice mechanicians, applied mathematicians, and engineers interested in (semi-)analytical approaches to fluid-structure interaction problems and the dynamics of complex mechanical systems involving rigid tanks partially filled with liquid.
