koordinaattiacceleration
koordinaattiacceleration, or coordinate acceleration, is a term used to describe the second time derivative of generalized coordinates in a chosen coordinate chart for a physical system. If a system is described by generalized coordinates q^i(t) with i = 1,...,n, then the velocity components are q̇^i and the coordinate accelerations are a^i = d^2 q^i/dt^2 = q̈^i.
In Cartesian coordinates on a flat space, the coordinate accelerations a^i correspond directly to the physical
Coordinate accelerations play a central role in dynamics formulated with generalized coordinates. In Lagrangian mechanics, the
Example: in polar coordinates (r, θ), the coordinate accelerations are q̈^r = r̈ and q̈^θ = θ̈, while the physical
See also: acceleration, generalized coordinates, curvilinear coordinates, Christoffel symbols, Euler–Lagrange equations.