The vector differential equation for light rays

2014 ◽  
pp. 837-840
Author(s):  
Christopher C. Davis
Keyword(s):  
Differential Equation ◽  
Light Rays ◽  
Vector Differential Equation

Solving the differential equation of light rays in Cartesian coordinates

Optik ◽  
2019 ◽  
Vol 194 ◽  
pp. 163055
Author(s):  
Xiaoli Ren ◽  
Jihong Wang ◽  
Ge Ren ◽  
Jia Zhai ◽  
Yufeng Tan ◽  
...  
Keyword(s):  
Differential Equation ◽  
Cartesian Coordinates ◽  
Light Rays

scholarly journals Spherical curves and quadratic relationships for special functions

1985 ◽  
Vol 27 (1) ◽  
pp. 111-124
Author(s):  
Even Mehlum ◽  
Jet Wimp
Keyword(s):  
Differential Equation ◽  
Hypergeometric Functions ◽  
Bessel Functions ◽  
Special Functions ◽  
Position Vector ◽  
Third Order ◽  
Generalized Hypergeometric Functions ◽  
Transcendental Functions ◽  
Horn Functions ◽  
Vector Differential Equation

AbstractWe show that the position vector of any 3-space curve lying on a sphere satisfies a third-order linear (vector) differential equation whose coefficients involve a single arbitrary function A(s). By making various identifications of A(s), we are led to nonlinear identities for a number of higher transcendental functions: Bessel functions, Horn functions, generalized hypergeometric functions, etc. These can be considered natural geometrical generalizations of sin2t + cos2t = 1. We conclude with some applications to the theory of splines.

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