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Online and downloadable PC-executable calculation utilities, including forward (direct) and inverse problems, in both two and three dimensions (accessed 2011-08-01). Online calculators with JavaScript source code by Chris Veness (Creative Commons Attribution license): Vincenty Direct (destination point) Vincenty Inverse (distance between points)
Orbital position vector, orbital velocity vector, other orbital elements. In astrodynamics and celestial dynamics, the orbital state vectors (sometimes state vectors) of an orbit are Cartesian vectors of position and velocity that together with their time () uniquely determine the trajectory of the orbiting body in space.
The path of this projectile launched from a height y 0 has a range d.. In physics, a projectile launched with specific initial conditions will have a range.It may be more predictable assuming a flat Earth with a uniform gravity field, and no air resistance.
The following notations are used very often in special relativity: Lorentz factor = where = and v is the relative velocity between two inertial frames.. For two frames at rest, γ = 1, and increases with relative velocity between the two inertial frames.
in calculations and experiments, it is lengths between two points or time intervals that are measured or of interest (e.g., the length of a moving vehicle, or time duration it takes to travel from one place to another),
An alternative formulation avoiding this problem (Golub & Van Loan 1996, §5.1.8) is implemented as the hypot function in many programming languages. The following Fortran code is a minimalistic implementation of Givens rotation for real numbers.
For certain problems, especially when used to analyze compressible flow in a duct or in case the flow is cylindrically or spherically symmetric, the one-dimensional Euler equations are a useful first approximation. Generally, the Euler equations are solved by Riemann's method of characteristics.
The two-dimensional stream function is based on the following assumptions: The space domain is three-dimensional. The flow field can be described as two-dimensional plane flow, with velocity vector