About the shperical coordinate

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In summary, The conversation involves solving a spherical pendulum problem and representing unit vectors in terms of Cartesian coordinates, which has already been done. The next step is to find the time derivatives of each unit vector, with θ and φ as functions of t. The problem has been solved by considering θ and φ as functions of t, while the unit vectors remain constant.
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General-Simon
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Here I am doing a spherical pendulum problem, and i was asked to represent the unit vectors of spherical coor in terms of Cartesian coor, which i have already solved:
r=sinθcosφ i + sinθsinφ j + cosθ k
θ=cosθcosφ i + cosθsinφ j - sinθ k
φ= -sinφ i + cosφ j
where φ is the angle on the X-Y plane, between x and the position, and θ is between position and z

now i want to know how to process to the next step: derive the time derivative of each unit vector, in terms of spherical unit vectors.
 
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  • #2
Just derive it
I don't know what's the problem
 
  • #3
netheril96 said:
Just derive it
I don't know what's the problem

ok, Thanks, I already solved it. considering the θ and φ also as the function of t, but the unit vectors do not.
 

1. What is the spherical coordinate system?

The spherical coordinate system is a three-dimensional coordinate system used to locate points in space. It uses two angles, typically denoted as θ and φ, and a distance r from the origin to define a point in space.

2. How is the spherical coordinate system different from the Cartesian coordinate system?

The spherical coordinate system uses angles and a distance from the origin, while the Cartesian coordinate system uses three perpendicular axes (x, y, z). In the spherical coordinate system, the angles represent the direction from the origin to the point, while the distance represents the magnitude of the vector.

3. What are the advantages of using the spherical coordinate system?

The spherical coordinate system is particularly useful for describing points in three-dimensional space that have a radial symmetry. It is also helpful for calculations involving spherical objects, such as planets or stars. Additionally, the spherical coordinate system can simplify certain mathematical operations, such as integration and differentiation.

4. How do you convert between spherical and Cartesian coordinates?

To convert from spherical to Cartesian coordinates, you can use the following equations:
x = r sinθ cosφ
y = r sinθ sinφ
z = r cosθ
To convert from Cartesian to spherical coordinates, you can use the following equations:
r = √(x2 + y2 + z2)
θ = arccos(z/r)
φ = arctan(y/x)

5. How is the spherical coordinate system used in scientific applications?

The spherical coordinate system is used in many scientific fields, including physics, astronomy, and engineering. It is particularly useful for describing the position and movements of celestial objects, such as planets and stars. In physics, the spherical coordinate system is often used in solving problems involving forces and fields, such as electromagnetic fields or gravitational forces.

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