Mathematics, 25.10.2019 20:43 gissellebramwell
Describe the geometric meaning of the following mappings in spherical coordinates.
(a) (rho, θ, ϕ) ↦ (rho, θ + π, ϕ)
(i)-there is a rotation by π around the y-axis.
(ii)-there is a rotation by π/2 about the z-axis.
(iii)-there is a rotation by π around the z-axis.
(iv)-there is a rotation by π around the x-axis.
(v)-there is a rotation by π/2 about the y-axis.
(b) (rho, θ, ϕ) ↦ (rho, θ, π − ϕ)
(i)-there is a rotation by π around the y-axis.
(ii)-there is a reflection across the xz plane.
(iii)-there is a reflection across the yz.
(iv)-there is a rotation by π around the x-axis.
(v)-there is a reflection across the xy plane.
(c) (rho, θ, ϕ) ↦ (2rho, θ + π/2 , ϕ)
(i)-there is a rotation by π 2 about the y-axis with a radial expansion by a factor of 2.
(ii)-there is a rotation by π 2 about the z-axis with a radial expansion by a factor of 2.
(iii)-there is a rotation by π about the z-axis.
(iv)-there is a rotation by π about the y-axis.
(v)-there is a rotation by π/2 about the x-axis with a radial compression by a factor of 1/2 .
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Describe the geometric meaning of the following mappings in spherical coordinates.
(a) (rho,...
(a) (rho,...
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