Exploring Uncommon Coordinate Systems in Physics

In summary: All of them are common each making use of symmetry of the system you are tackling. That's the reason why you learn them in your curriculum.
  • #1
Falgun
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I have come across Cartesian, Polar, Cylindrical & Spherical Coordinate Systems so far and was wondering if someone could tell me which are the uncommon systems used in physics which everyone says that they exist but no one explicitly mentions. Is there a "standard reference" or are they just passed down as word of mouth? Sorry if the question is a bit misguided because I have no idea about this topic.
 
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  • #2
All of them are common each making use of symmetry of the system you are tackling. That's the reason why you learn them in your curriculum.
 
  • #3
anuttarasammyak said:
All of them are common each making use of symmetry of the system you are tackling. That's the reason why you learn them in your curriculum.
I understand that. I am asking if you could name and explain some uncommon ones?
 
  • #4
As a short example skew coordinates. In GR metric tensor ##g_{ij}## defines what coordinate system the system has.
 
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Parabolic coordinates are of some use in the Coulomb-scattering problem in quantum mechanics and for the bound state problem when treating the Stark effect. They are always a good choice if you have a spherically symmetric problem in a situation, where some direction is preferred by the physical situation. In the scattering problem that's the direction of the incoming-particle momentum; in the case of the Stark effect it's the direction of the external electric field.

These 3D orthogonal coordinates are the ones for which the 3D Laplace operator and thus the Helmholtzoperator separates. For a thorough treatment, see the great books by Morse and Feshbach, Methods of Theoretical Physics (2 vols.).
 
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  • #9
Most coordinate systems have no name. They are described by their mathematical properties instead. These can be equations to transform from named systems to the unnamed system or the metric written in the new coordinates.
 
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  • #10
Falgun said:
I have come across Cartesian, Polar, Cylindrical & Spherical Coordinate Systems so far and was wondering if someone could tell me which are the uncommon systems used in physics which everyone says that they exist but no one explicitly mentions. Is there a "standard reference" or are they just passed down as word of mouth? Sorry if the question is a bit misguided because I have no idea about this topic.

Moon and Spencer's "Field Theory Handbook" is a compendium of 40 coordinate systems, providing separation equations and solutions for the Laplace and Helmholtz equations in each.
 
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  • #11
If you study geodesy using Heiskanen and Moritz, you will run into elliptic coordinates pretty extensively
 
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  • #12
Andy Resnick said:
Moon and Spencer's "Field Theory Handbook" is a compendium of 40 coordinate systems, providing separation equations and solutions for the Laplace and Helmholtz equations in each.
There are many different coordinate systems to choose from. If the shape of the object is deliberately designed to correspond to these special coordinate systems in the engineering design, this may simplify the analysis and speed up the efficiency of the simulation calculation.
 
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  • #13
The ##\mathrm{H}_2^+## molecular hamiltonian is separable in elliptical coordinates.
 
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  • #14
How about Rindler coordinates in SR?
 
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  • #16
In mechanical dynamics the 'tangential & normal' component system is often used since in curvilinear motion acceleration is thereby relatively simply represented.
 
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1. What are uncommon coordinate systems in physics?

Uncommon coordinate systems in physics refer to coordinate systems that are not commonly used in traditional physics equations and calculations. These include non-Cartesian coordinate systems, such as polar, cylindrical, and spherical coordinates, as well as more complex systems like curvilinear and generalized coordinates.

2. Why are uncommon coordinate systems important in physics?

Uncommon coordinate systems are important in physics because they allow us to describe and analyze physical phenomena in a more efficient and accurate manner. They are particularly useful in situations where traditional Cartesian coordinates are not suitable, such as in systems with spherical or cylindrical symmetry.

3. How do uncommon coordinate systems differ from Cartesian coordinates?

Uncommon coordinate systems differ from Cartesian coordinates in that they use different variables to describe the position and orientation of objects in space. For example, polar coordinates use the distance from a central point and the angle from a reference direction, while Cartesian coordinates use the x, y, and z axes.

4. What are some applications of uncommon coordinate systems in physics?

Uncommon coordinate systems have various applications in physics, including in electromagnetism, fluid dynamics, and quantum mechanics. For instance, polar coordinates are commonly used in analyzing circular motion and electromagnetic fields, while curvilinear coordinates are used to describe the behavior of fluids in non-Cartesian geometries.

5. How can I learn more about uncommon coordinate systems in physics?

There are many resources available for learning about uncommon coordinate systems in physics, including textbooks, online tutorials, and academic papers. It is also helpful to have a strong understanding of vector calculus and coordinate transformations in order to fully grasp and apply these systems in physics problems.

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