Me 230 kinematics and dynamics university of washington. The latter distance is given as a positive or negative number depending on which side of the reference plane faces the point. A point can be represented with, in cubic coordinates, with, in cylindrical coordinates and with. The cylindrical coordinate system is used in cases where the particle moves along a 3d curve.
Frames of references in order to really look at particle dynamics in the context of the atmosphere, we must now deal with the fact that we live and observe the weather in a noninertial reference frame. Polar coordinates d no real difference all are bad. Convert the following equation written in cartesian coordinates into an equation in cylindrical coordinates. If the particle is constrained to move only in the r q plane i. Now in my fluid dynamics notes i found the following expressions for the dissipation. Based on a control volume analysis for the dashed box, answer the following.
Consider a steady, incompressible boundary layer with thickness. Coordinate systems advanced dynamics wiley online library. The fundamental plane of the system contains the observer and the horizon. Spherical coordinate system r me101 division iii kaustubh dasgupta 1. An example of a curvilinear coordinate system which is not orthogonal is provided by the system of elliptical cylindrical coordinates see tutuorial 9. Dynamics lecture4 cylindrical components free download as powerpoint presentation. Cartesian coordinate system cylindrical coordinate system spherical coordinate system.
Three commonly used coordinate systems to describe this motion. It is often helpful to translate a problem from one coordinate system to another depending on the nature of the problem. A cylindrical coordinate system is a threedimensional coordinate system that specifies point positions by the distance from a chosen reference axis, the direction from the axis relative to a chosen reference direction, and the distance from a chosen reference plane perpendicular to the axis. Specially, we will look at a rotating coordinate system and introduce the coriolis. An internet book on fluid dynamics continuity equation in other coordinate systems we recall that in a rectangular cartesian coordinate system the general continuity equation is. We shall see that these systems are particularly useful for certain classes of. A point p in the plane can be uniquely described by its distance to the origin r distp. The distance is usually denoted rand the angle is usually denoted. Using a polar coordinate system for the formulation. Pdf analytical solution of direct dynamics problem in. Dynamics lecture4 cylindrical components euclidean. The cylindrical coordinate system extends polar coordinates into 3d by using the standard vertical coordinate z. We simply add the z coordinate, which is then treated in a cartesian like manner.
In this case, the path is only a function of f r ma. Many flows which involve rotation or radial motion are best described in cylindrical. Cylindrical coordinates transforms the forward and reverse coordinate transformations are. A polar coordinate system is a 2d representation of the cylindrical coordinate system. Recently the dynamics of ellipsoidal galaxies has been. Top 15 items every engineering student should have. Unit vectors the unit vectors in the cylindrical coordinate system are functions of position.
Continuity equation in cylindrical polar coordinates. Consider the solution using the cylindrical coordinate system. Here the radial coordinate is constant, the transverse coordinate increases with time as the girl rotates about the vertical axis, and her. When the particle moves in a plane 2d, and the radial distance, r, is not constant, the polar coordinate system can be used to express the path of motion of. While the horizon is an intuitively obvious concept, a. Cylindrical coordinates simply combine the polar coordinates in the xy plane with the usual z coordinate of cartesian coordinates. The coordinate system in such a case becomes a polar coordinate system. Pdf in this study, the analytical solution of the direct dynamics problem that mostly requires. The local material coordinate system of the reinforced tape layers is designated as l, t, r, where l is the wound direction, t is the direction perpendicular to the aramid wire in. Space curvilinear motion indian institute of technology. It is possible to use the same system for all flows. Chapter 1 governing equations of fluid flow and heat transfer. A hard problem in one coordi nate system may turn out to be. We introduce cylindrical coordinates by extending polar coordinates with theaddition of a third axis, the zaxis,in a 3dimensional righthand coordinate system.
In the nt coordinate system, the origin is located on the particle the origin moves with. Acceleration in the nt coordinate system ii there are two components to the acceleration vector. The cylindrical coordinate system can be used to describe the motion of the girl on the slide. In this chapter we will describe a cartesian coordinate system and a cylindrical coordinate system. Fluid mechanics problems for qualifying exam fall 2014 1. Calculus ii cylindrical coordinates practice problems. These three coordinate systems cartesian, cylindrical, spherical are actually only a subset of a larger group of coordinate systems we call orthogonal coordinates.
Advanced fluid dynamics 2017 navier stokes equation in curvilinear coordinate systems 1. Cartesian coordinates consist of a set of mutually perpendicular axes, which intersect at a common point, the origin. Advanced fluid dynamics 2017 navier stokes equation in. We will present polar coordinates in two dimensions and cylindrical and spherical coordinates in three dimensions. There are a total of thirteen orthogonal coordinate systems in which laplaces equation is separable, and knowledge of their existence see morse and feshbackl can be useful for solving problems in potential theory. In this lecture, we will look at some other common systems of coordinates.
Cartesian coordinates, cylindrical coordinates etc. Ex 3 convert from cylindrical to spherical coordinates. The vector k is introduced as the direction vector of the zaxis. Analytical solution of direct dynamics problem in cylindrical coordinates. In your past math and physics classes, you have encountered other coordinate systems such as cylindrical polar coordinates and spherical coordinates. Fluid dynamics dissipation using cylindrical coordinates. Pdf analytical solution of direct dynamics problem in cylindrical. Polar coordinates the polar coordinate system is a twodimensional coordinate system in which the position of each point on the plane is determined by an angle and a distance. When a pilot flies an airplane in a vertical loop of constant radius r at constant speed v, his apparent weight is maximum at. Altazimuth coordinate system the altitudeazimuth coordinate system is the most familiar to the general public.