How do you convert Cartesian to spherical coordinates?
To convert a point from spherical coordinates to Cartesian coordinates, use equations x=ρsinφcosθ,y=ρsinφsinθ, and z=ρcosφ. To convert a point from Cartesian coordinates to spherical coordinates, use equations ρ2=x2+y2+z2,tanθ=yx, and φ=arccos(z√x2+y2+z2).
What is the longitudinal axis of a cylinder?
The origin of the system is the point where all three coordinates can be given as zero. The axis is variously called the cylindrical or longitudinal axis, to differentiate it from the polar axis, which is the ray that lies in the reference plane, starting at the origin and pointing in the reference direction.
What is cylindrical polar coordinates system?
Cylindrical coordinates are a simple extension of the two-dimensional polar coordinates to three dimensions. The polar coordinate r is the distance of the point from the origin. The polar coordinate θ is the angle between the x-axis and the line segment from the origin to the point.
What is longitudinal and transverse axis?
Longitudinal – spanning the length of a body. Orthogonal – at a right angle (at the point of intersection). Parallel – in the same direction. Transverse – intersecting at any angle, i.e. not parallel.
Is the longitudinal axis the same as the vertical axis?
The longitudinal axis runs from the nose of the aircraft to the tail. This is the axis around which the aircraft rolls (Fig. 8). The vertical axis is slightly different to the others, running vertically through the center of the aircraft.
How many planes are there in cylindrical coordinate system?
three coordinate surfaces
The cylindrical coordinate system is illustrated in Fig. 3.20. The three coordinate surfaces are the planes z = constant and θ = constant, with the surface of the cylinder having radius r. For the Cartesian system, in contrast, all three coordinate surfaces are planes.
What is the Del operator in cylindrical coordinates?
To convert it into the cylindrical coordinates, we have to convert the variables of the partial derivatives. In other words, in the Cartesian Del operator the derivatives are with respect to x, y and z. But Cylindrical Del operator must consists of the derivatives with respect to ρ, φ and z.