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The Cartesian components of the position vector r in a general coordinate system are given by 1 1 = uv cos 6, y = uv sin ø, z=;(u² – v²), where (u, v, ø) are known as paraboloidal coordinates. We shall choose { = u, &² = v and F³ = 6. 1.) Find the covariant and contravariant base vectors corresponding to the paraboloidal coordinates. Is the coordinate system orthonormal, orthogonal or neither?

The Cartesian components of the position vector r in a general coordinate system are given by 1 1 = uv cos 6, y = uv sin ø, z=;(u² – v²), where (u, v, ø) are known as paraboloidal coordinates. We shall choose { = u, &² = v and F³ = 6. 1.) Find the covariant and contravariant base vectors corresponding to the paraboloidal coordinates. Is the coordinate system orthonormal, orthogonal or neither?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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The Cartesian components of the position vector r in a general coordinate system are given by 1 1 = uv cos 6, y = uv sin ø, z=;(u² – v²), where (u, v, ø) are known as paraboloidal coordinates. We shall choose { = u, &² = v and F³ = 6. 1.) Find the covariant and contravariant base vectors corresponding to the paraboloidal coordinates. Is the coordinate system orthonormal, orthogonal or neither?
Transcribed Image Text:The Cartesian components of the position vector r in a general coordinate system are given by 1 1 = uv cos 6, y = uv sin ø, z=;(u² – v²), where (u, v, ø) are known as paraboloidal coordinates. We shall choose { = u, &² = v and F³ = 6. 1.) Find the covariant and contravariant base vectors corresponding to the paraboloidal coordinates. Is the coordinate system orthonormal, orthogonal or neither?
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