- #1
queenstudy
- 101
- 0
can i get some help in how i can convert from cartesian to cylindrical and spherical unit vectors and vice versa ? thank you
queenstudy said:i mean with proofs because i already read that website page
queenstudy said:yes
in the definition of unit vectors how did we get the cartesian coordinates in terms of cylinderical coordinates
queenstudy said:yes please because we know how the opposite happens
queenstudy said:i know how raw and phy are in terms of x hat and y hat how did you change that to the last line I am still not getting the idea??
Cartesian, cylindrical, and spherical unit vectors are three different coordinate systems used to describe the position of a point in space. Cartesian coordinates use x, y, and z axes to represent the position of a point, while cylindrical coordinates use a radius, angle, and height, and spherical coordinates use a radius, inclination, and azimuth.
Converting from Cartesian to cylindrical or spherical coordinates can be useful when working with different coordinate systems or when solving certain types of mathematical problems. Some applications, such as physics or engineering, may require working with different coordinate systems to describe the position of objects in space.
To convert from Cartesian to cylindrical coordinates, you can use the following equations:
r = √(x² + y²)
θ = arctan(y/x)
z = z
To convert from Cartesian to spherical coordinates, you can use these equations:
r = √(x² + y² + z²)
φ = arctan(√(x² + y²)/z)
θ = arctan(y/x)
Yes, when converting to cylindrical or spherical coordinates, it is important to be aware of the range of values for each coordinate. For example, in cylindrical coordinates, the angle θ should be between 0 and 2π, and the height z can be any real number. In spherical coordinates, the inclination φ should be between 0 and π, and the azimuth θ should be between 0 and 2π.
Yes, you can also convert back from cylindrical or spherical coordinates to Cartesian coordinates. To convert from cylindrical to Cartesian coordinates, you can use these equations:
x = r cos(θ)
y = r sin(θ)
z = z
To convert from spherical to Cartesian coordinates, you can use these equations:
x = r sin(φ) cos(θ)
y = r sin(φ) sin(θ)
z = r cos(φ)