To passengers in plane a, however, plane b appears to be flying sideways and moving due south. Kinematics of a particle university of central oklahoma. In the limit, this reduces to the general geometrically conservative expression for the divergence in the curvilinear coordinates. Only one degree of freedom is needed in order to give the position in any instant. Readers who are already wellversed in functional analysis will probably find more rigorous manuscripts such as 14 more suitable. A typical nt problem will either give the exact location of the particle on a path, or it will give kinematics information from which the position can be determined. Me 2580 dynamics curvilinear motion rectangular components general concepts. In the nt coordinate system, the origin is located on the particle the origin moves with the particle. Rectangular components motion of a projectilenext lecture. The presentation here closely follows that in hildebrand 1976.
Recognizing objects from curvilinear motion article pdf. Since this path is often described in three dimensions, vector. Rectangular motion is useful if a x depends only on t, x, andor v x likewise for a y and a z. Tensor analysis and curvilinear coordinates phil lucht rimrock digital technology, salt lake city, utah 84103 last update. Since the motion is often threedimensional, vectors are used to describe the motion.
In the n tcoordinate system, the origin is located on the particle the origin moves with the particle. Curvilinear motion is defined as motion that occurs when a particle travels along a curved path. Since this path is often described in three dimensions, vector analysis will be used to formulate the particles position, velocity, and acceleration. Gradient, divergence and curl in curvilinear coordinates. The curved path can be in two dimensions in a plane, or in three dimensions. Normaltangential nt coordinates are attached to, and move with, a particle. Relationships between linear and angular motion body segment rotations combine to produce linear motion of the whole body or of a specific point on a body. Threedimensional curvilinear motion describes the most general case of motion for a particle. This type of motion is more complex than rectilinear straightline motion. In this section we will study the motion of particles that are restricted to move in a 2d plane.
Given rt the position vector of a particle p, the velocity and acceleration of p are defined to be dr v dt and dv a dt. The taxis is tangent to the path curve at the instant considered, positive in the direction of the particles motion. Abduljalil alabidi thermodynamics mechatronics engineering department pet121 general curvilinear motion curvilinear motion occurs when a particle moves along a curved path. For easy handling, resolve the motion into x and y components and use the formulas in rectilinear translation. Some examples of curvilinear motion are as follows. These are two important examples of what are called curvilinear coordinates.
Since the motion is often threedimensional, vectors are usually used to describe the motion. If the particle has a velocity v at time t and a velocity v. Top 15 items every engineering student should have. S4general curvilinear motion university of alabama. Treating bodies as particles is, of course, an idealization which involves an approximation. Curvilinear motion article about curvilinear motion by. A particle moves along a curve defined by the path function, s. If you are completely new to the subject of general curvilinear coordinates or if you seek guidance on the basic machinery associated with nonorthonormal.
When the radius of curvature r of the trajectory remains constant, the trajectory is a circumference and the motion is circular, as in the case shown in figure 3. Thus, the position vector will be a function of time, i. General curvilinear curvilinear motion motion application. Note that the equations describing the motion in each coordinate direction are identical to those of linear motion, as denoted in the position, velocity, acceleration section. We think of a particle as a body which has mass, but has negligible dimensions. A slotted link on a fixed pivot causing a rod to slide along the curve is an example of curvilinear motion. Cartesian coordinates we will start by studying the motion of a particle. For example in lecture 15 we met spherical polar and cylindrical polar coordinates. Curvilinear motion describes the motion of a moving particle that conforms to a known or fixed curve. Since this path is often described in three dimensions, vector analysis. Curvilinear translation projectile motion the vertical component of projectile is under constant gravitational acceleration and the horizontal component is at constant velocity. Def dynamics and dynamical systems solved problems 3. In curvilinear motion the trajectories of individual particles of the body are curved, although the orientation of the body in space does not change. Both the magnitude and direction of r may vary with time.
A particle moving along a curved path undergoes curvilinear motion. Most particles experience curvilinear motion in three dimensions. In rectilinear motion all particles of the body travel the same distance along parallel straight lines. The formalism of curvilinear coordinates provides a unified and general description of the standard coordinate systems.
Curvilinear velocity and acceleration are found given the position of the particle with respect to time. In general, this particle will not be still, but its position will change in time. In this section the general aspects of curvilinear motion are discussed, and in the. Therefore there is no position vector in nt coordinates. Curvilinear motion general curvilinear motion curvilinear motion is defined as motion that occurs when a particle travels along a curved path.
The passenger plane a is flying east with a velocity of 620 kmh when a smaller aircraft b passes underneath heading southeast in the direction shown. The position of the particle at any instant is designated by the vector r rt. The motion of the particles will be analyzed though kinematic analysis i. How to solve any projectile motion problem the toolbox method. Important special case of plane curvilinear motion radius of curvature becomes constant radius r of the circle. If theequation of the path is y x210, determine the magnitude and x2direction of the velocity and the acceleration when t 2 s. A car driver enters a curve at 72 kmh, and slows down, making the speed decrease at a constant rate of 4. General curvilinear motion a particle moving along a curved path undergoes curvilinear motion.
Position, velocity, and acceleration if a particle does not move in a straight line, then its motion is said to be curvilinear. Since this path is often described in three dimensions, vector analysis will be used to formulate the particles position, velocity. Both the magnitude and direction of rmay vary with time. Same as that obtained with n and tcomponents, where the. The study of such motion involves the use of two coordinate systems, the first being planar motion and the latter.
The sides of the small parallelepiped are given by the components of dr in equation 5. If all motion components are directly expressible in terms of horizontal and vertical coordinates 1 also, dydx tan. Curvilinear coordinates are often used to define the location or distribution of physical quantities which may be, for example, scalars, vectors, or tensors. Determine the actual velocity of b and the velocity which b appears to have. These scenes include various motion patterns of crowded people, such as splitting, merging, intersecting, crossing, linear motion, curvilinear motion, circular motion, emergency collection, evacuation, and so. Curvilinear translation projectile motion engineering. Curvilinear motion acceleration components duration. Unlike other approaches that seek to recognize particular motions. For motion in a circular path, r is constant the components of velocity and acceleration become. Linear motion can be further divided to rectilinear motion and curvilinear motion.