Differensialer

Differensialer is a term used for two related concepts in mathematics and mechanical engineering. In mathematics, a differential describes an infinitesimal change in a variable and is fundamental to differential calculus. In mechanics, a differential gear transmits engine torque to wheels while allowing them to rotate at different speeds.

Mathematical differentials: For a function y = f(x), the differential dy is defined as f′(x) dx, where dx represents an infinitesimal change in x. For multivariable functions, the total differential is dy = ∑ (∂f/∂x_i) dx_i, summing over all input variables. Differentials provide a linear approximation to changes in f and underpin the concept of differential forms and integration.

Mechanical differentials: The differential gear splits torque between two driven wheels and allows them to rotate at different speeds, which is essential when the vehicle moves through curves. Types include open differentials, which distribute torque based on wheel resistance; limited-slip differentials, which reduce excessive slip to improve traction; and locking differentials, which force equal wheel speeds for off‑road use. Modern systems may combine mechanical design with electronic controls to optimize traction and stability.

Other contexts: The idea of a differential appears in differential equations, where rates of change are related to variables, and in differential signaling in electronics, where information is encoded by the difference between two signals. In all uses, differentials capture the notion of small changes or contrasts between paired quantities, forming a core concept across disciplines.