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2016•Unpublished venueRequires access

Spherical Polar Coordinates

Mark Ladd

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Abstract

In Fig. A6.1, the spherical polar coordinates (aka polar coordinates) r, θ and ϕ are given by: where The volume element dτ in Fig. A6.1 corresponds to the infinitesimal quantity dxdydz in Cartesian coordinates; it is straightforward to show the relationship: The limits of the polar variables that correspond to x, y and z each between − ∞ and + ∞ are: Convert the following Cartesian coordinates to spherical polar coordinates. (Answer at end of Appendices.)

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What this paper is about

In Fig. A6.1, the spherical polar coordinates (aka polar coordinates) r, θ and ϕ are given by: where The volume element dτ in Fig. A6.1 corresponds to the infinitesimal quantity dxdydz in Cartesian coordinates; it is straightforward to show the relationship: The limits of the polar variables that correspond to x, y and z each between − ∞ and + ∞ are: Convert the following Cartesian coordinates to spherical polar coordinates. (Answer at end of Appendices.)

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Available abstract

In Fig. A6.1, the spherical polar coordinates (aka polar coordinates) r, θ and ϕ are given by: where The volume element dτ in Fig. A6.1 corresponds to the infinitesimal quantity dxdydz in Cartesian coordinates; it is straightforward to show the relationship: The limits of the polar variables that correspond to x, y and z each between − ∞ and + ∞ are: Convert the following Cartesian coordinates to spherical polar coordinates. (Answer at end of Appendices.)

Key concepts: Log-polar coordinates, Orthogonal coordinates, Cartesian coordinate system, Generalized coordinates, Bipolar coordinates, Prolate spheroidal coordinates, Polar coordinate system, Polar

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