drdt

drdt is a notation used to denote the derivative of a quantity r with respect to time t. In formal writing this derivative is usually written as dr/dt, but in plain-text contexts it may appear as drdt. The concept expresses how r changes over time and is a fundamental building block in calculus, physics, and differential equations.

If r is a scalar function of time, dr/dt represents the instantaneous rate of change of r with respect to time. If r is a vector-valued function, such as a position vector r(t) in space, then dr/dt is the velocity vector of the moving object. The magnitude |dr/dt| gives the speed, while the direction of dr/dt indicates the direction of motion. In kinematics, v(t) = dr/dt is a central relation between position and velocity.

In polar, cylindrical, or spherical coordinates, r often denotes a radial distance. Here dr/dt is the radial component of the velocity, while angular components involve additional factors such as r dθ/dt in two-dimensional polar coordinates or more complex expressions in higher dimensions. These decompositions help analyze motion in curved or rotating frameworks.

In the context of differential equations, dr/dt appears in rate equations, growth models, and dynamical systems. Solutions require initial conditions like r(t0) = r0 and may describe how r evolves over time under given rules or influences.

Notation variants include ∂r/∂t for functions with multiple variables, or dr/dt as a part of larger expressions. While drdt is common in plain text, the slash form dr/dt remains standard in formal writing.