Think in a sphere with radius and two antipodal points of it wich we call the North pole and the South pole. Meridians are great circles passing through the . A loxodrome is a curve on the sphere intersecting all meridians at the same angle.
where and are constants, is an equation of loxodromes in the Gaussian coordinates .
We denote , whence the equation of the family (1) in the parameter plane reads
When we denote also the position vector of a point of the sphere by
we have the tangent vector of a curve (1) on the sphere:
we can write the tangent vector of the curve as
For a tangent vector of a meridian, the partial derivative may be taken. Thus we obtain the value
which is a constant. It means that the angle between the curve (1) and a meridian is constant.
Pictures in http://hu.wikipedia.org/wiki/LoxodromaWiki
|Date of creation||2013-03-22 19:11:02|
|Last modified on||2013-03-22 19:11:02|
|Last modified by||pahio (2872)|