Sharif Digital Repository

Based on Lagrangian mechanics, use of velocity constraints as a special set of quasi-velocities helps derive explicit equations of motion. The equations are applicable to holonomic and nonholonomic constrained multibody systems. It is proved that in proposed quasi-spaces, the Lagrange multipliers are eliminated from equations of motion; however, it is possible to compute these multipliers once the equations of motion have been solved. The novelty of this research is employing block matrix inversion to find the analytical relations between the parameters of quasi-velocities and equations of motion. In other words, this research identifies arbitrary submatrices and their effects on equations... 

It is well-known that helicopters descending fast may enter the so-called Vortex Ring State (VRS), a region in the velocity space where the blade's lift differs significantly from regular regions and high amplitude fluctuations are often present. These fluctuations may lead to instability and, therefore, this region is avoided, typically by increasing the horizontal speed. This paper researches this phenomenon in the context of small-scale quadcopters. The region corresponding to the VRS is identified by combining first-principles modeling and wind-tunnel experiments. Moreover, we propose that the so-called Windmill-Brake State (WBS) or autorotation region should also be avoided for...