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Caroline
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What is the hyper-cylindrical line element?
What is the hyper-cylindrical line element?
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- Thread starter Caroline
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In summary, the conversation revolves around the search for the hyper-cylindrical line element, specifically in the context of sound wave propagation in the real projective space RP3. The person asking the question is struggling to find this element and is seeking help from others who may have knowledge or resources on it. The background and previous research on this topic is mentioned, as well as the individual's qualifications and goals.
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Nugatory
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You will get better answers if you can tell us a bit more. Where did you come across the term? What parts of the discussion there made sense to you and what parts left you confused? You'll get a bunch of hits if you google for "hypercylindrical line element" - do they help, and if not, what more specific questions do they leave you with?Caroline said:
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Caroline
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I am trying to describe sound wave propagation in the real projective space RP3. This procedure has been done for sound wave propagation on a background in a medium with the background topology of RP2 - using a line element with cylindrical coordinates. The FULL cylindrical line element is easily found.. and as shown below in the spacetime metric of an anisotropic uniaxial system in three-dimensions. I am looking for the FULL hyper-cylindrical line element --- and am having a lot of trouble finding it! just looking to see if anyone knows of it.
Signed, Mechanical engineer / Materials Science Phd student striving for a theory..
Signed, Mechanical engineer / Materials Science Phd student striving for a theory..
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1. What is a hyper-cylindrical line element?
A hyper-cylindrical line element is a mathematical representation of a line in a four-dimensional space. It takes into account both space and time, and is often used in the study of general relativity and cosmology.
2. How is a hyper-cylindrical line element different from a regular line element?
A hyper-cylindrical line element takes into account the curvature of space-time, while a regular line element only considers the distance between two points in a flat space. It is a more complex and accurate representation of a line in four-dimensional space.
3. What are the main components of a hyper-cylindrical line element?
The main components of a hyper-cylindrical line element are the metric coefficients, which describe the space-time curvature, and the coordinates, which determine the location of a point in space and time. It also includes a constant, c, which represents the speed of light.
4. How is a hyper-cylindrical line element used in physics?
A hyper-cylindrical line element is used in physics to describe the paths of objects moving in a curved space-time, such as planets orbiting around a star or particles in a black hole. It is also used in the study of general relativity and cosmology to understand the behavior of the universe.
5. Can a hyper-cylindrical line element be applied to other dimensions?
Yes, a hyper-cylindrical line element can be applied to any number of dimensions, although it is most commonly used in four-dimensional space-time. It can also be adapted to describe different types of geometries, such as spherical or hyperbolic.
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