Zeitveränderlich

Zeitveränderlich is a German term that translates to "time-varying" or "time-dependent" in English. It is used in various fields, including physics, engineering, economics, and mathematics, to describe phenomena, parameters, or systems whose properties change over time.

In physics, a time-varying quantity might refer to a force that is not constant, a velocity that is accelerating or decelerating, or a magnetic field whose strength is changing. For instance, in electromagnetism, Faraday's law of induction states that a changing magnetic flux through a loop induces an electromotive force, highlighting the time-varying nature of the magnetic field.

In engineering, a time-varying system could be one where its characteristics, such as resistance or capacitance, drift over time due to wear and tear or environmental conditions. Control systems are often designed to account for time-varying elements to maintain desired performance.

Economically, time-varying models might represent fluctuating interest rates, changing inflation, or market conditions that evolve. The analysis of such systems often involves differential equations or other mathematical tools that can capture the temporal evolution of variables.

Mathematically, a function is considered time-varying if its output depends not only on its input variables but also explicitly on time. This is in contrast to time-invariant systems or functions where the relationships between inputs and outputs remain constant regardless of when they are observed. Understanding whether a system or parameter is time-varying is crucial for accurate modeling, prediction, and control.