There is a growing need for smaller, more economic transportation systems. Personal transportation systems such as hover boards and Segways have made their way onto the market. The two-wheeled configuration of the Segway is a two-wheeled inverted pendulum system. This paper derives the equations of motion of an inverted wheeled pendulum system and a double inverted wheeled pendulum system. The equations are derived using the Euler-Lagrange equations. The first configuration derived is of the single inverted pendulum system. The second configuration derived adds on another inverted pendulum system similar to the first configuration, along with more variables and constraints. The results of this paper provide valuable information about the equations of motion of a Segway. The methods described in this paper lay the groundwork for numerous possible future studies that may investigate the motion of a two-wheeled pendulum system.
INTRODUCTION The study of fluid flow around cylinders is not a new topic of interest. It has come to be one of the classical problems of fluid mechanics. Cylinder-like architecture can be found in an array of things such as heat exchangers, cooling systems, cables, buildings and anything regarding air-flow and/or water-flow. Numerous studies have been done where the disturbance of cylinders in a close range can cause “significant changes in parameters of the aerodynamic characteristics, such as fluctuating lift and drag forces, time-averaged and fluctuating pressure distributions, Strouhal number, and vortex shedding patterns, when the spacing between the cylinders is changed,” and all at a broad spectrum of Reynolds’ numbers. However, there are very few instances in which two cylinders will be perfectly aligned and our literature review findings reflect that. Nevertheless, many interesting discoveries uncovered in our search. For instance, a study done by Carmo investigates the two- and three-dimensional numerical solutions of flow around pairs of cylinders. His findings state that for Reynolds numbers greater than 190, two-dimensional simulations are not sufficient enough to predict the Reynolds number to centre-to-centre pair of drag inversion . In a somewhat similar fashion, another study investigates the fluctuating forces acting on two square prisms in a turbulent boundary layer in numerous arrangements. Sakamoto’s findings declare that phase relationships exist between the fluctuating lift of the two prisms and the phase shift is proportional to the distance between the prisms .Although our simulations only investigate an arrangement of two cylinders, a study done by Price had an interesting find. His study investigated the fluid forces acting on a single cylinder in groups of two and three cylinders. His findings affirm that “the effect of cylinder displacement on the fluid forces of one cylinder in a group of three is very similar to that obtained with one cylinder in a group of two” . One study even focused on the analysis others had performed in the past 10-20 years on finite flow around two “infinite” cylinders. Surprisingly, in Sumner’s comprehensive review of the literature of flow around two circular cylinders of with the same diameter, his findings state that a “deeper insight into the flow physics will arise from more accurate numerical simulations at higher Reynolds number; however there is a general lack of experimental data at low Reynolds number to assist with the validation of current numerical simulations” . Investigating the fluid flow around cylinders can provide a better understanding of the fluid forces in instances where more complex arrangements are involved. In our report, we investigate a way to reduce the fluid forces acting on two circular cylinders in a tandem arrangement exposed to an incompressible, turbulent fluid flow by changing the distance between the cylinders.