This book presents a new scientific discovery about the nonlinear instability and inertial coupling effects for aircrafts, land vehicles, and ships. It focuses on the dynamic instability and inertial couplings of the rotational motions of these vehicles and provides analytical solutions for the nonlinear governing equations without linearization. A nonlinear stability theorem is proven analytically, numerically, and experimentally. The threshold for the nonlinear instability is given. The book covers topics such as the fundamental mistakes in automotive, aviation, and naval architecture industries; energy flow patterns of aircrafts, ships, land vehicles, and rigid body torque-free motion; the nonlinear solution of vehicle dynamics; nonlinear instabilities and inertial coupling effects of ships, aircrafts, and land vehicles. It reveals the mechanism of broaching and capsizing of ships; a phase locked-in phenomenon for ships; Dutch roll, wing rock, Pilot-Induced-Oscillation, and upset of aircrafts including un-commanded roll, pitch, and yaw; and rollover of land vehicles. The unique feature of this book is to provide scientific analyses and explanations for the root causes for two aircraft incidents and 16 aircraft crashes based on their FDR data, for two Ro/Ro ship capsizes, two cruise ship capsizes. An inertial coupling factor is proposed to measure the effect of the inertial coupling. A dynamic stability factor is proposed to indicate how dynamically stable a vehicle is. This book provides evidences based on the analytical analyses, the numerical simulations, the physical experiments, and the highway fatality data to prove that the Anti-Brake System and Electronic Stability Control cause more rollovers and fatalities. The autopilot of aircrafts is proven to cause some nonlinear instabilities and crashes. Three recipes for aircraft crashes during takeoff, landing approach, and cruise leveling are given. A mechanical demonstrator is also given.

The equations of motion for a ship pitching and rolling in a calm sea were found to be coupled by means of a second order term in the rolling equation of motion. When the pitching motion is simple harmonic the equation of motion in roll is of the Mathieu type, the two independent parameters being pitching amplitude and frequency. The stability diagram of the Mathieu equation including the effect of linear damping is determined theoretically and verified by solving the Mathieu equation on an analogue computer. In experiments with one ship model form, it was found that the transition from stable to unstable motion occurred for the value of the parameters predicted by the theory, and that the rolling motions obtained experimentally closely resembled the computer solutions. It was concluded that (1) unstable rolling motions are possible for very small pitching amplitudes, (2) when the natural frequency of pitch is twice that of roll the amplitude required to produce unstable motion is a minimum, and (3) for any pitching frequency, the greater the amount of damping, the greater the amplitude of pitching must become to produce unstable rolling motions. (Author).

A study was made to determine the feasibility of programing an analog simulation of aircraft stability on a general-purpose analog computer using non-linear differential equations. The simulation was to demonstrate the effects of inertial cross-coupling. An F-4 aircraft was simulated at two different reference flight conditions using the equations derived in the study. (Author).

This book presents a study of the stability of mechanical systems, i.e. their free response when they are removed from their position of equilibrium after a temporary disturbance. After reviewing the main analytical methods of the dynamical stability of systems, it highlights the fundamental difference in nature between the phenomena of forced resonance vibration of mechanical systems subjected to an imposed excitation and instabilities that characterize their free response. It specifically develops instabilities arising from the rotor–structure coupling, instability of control systems, the self-sustained instabilities associated with the presence of internal damping and instabilities related to the fluid–structure coupling for fixed and rotating structures. For an original approach following the analysis of instability phenomena, the book provides examples of solutions obtained by passive or active methods.