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Physics에서 Coordinate Transformation 📂Mathematical Physics

Physics에서 Coordinate Transformation

Definition

Two-dimensional coordinate systems (x1,…,xn)(x_{1}, \dots, x_{n}) and (x1′,…,xn′)(x_{1}^{\prime}, \dots, x_{n}^{\prime}) are related by the following functions f1,…,fnf_{1}, \dots, f_{n} (or the act of changing coordinates itself) is referred to as a coordinate transformation from (x1,…,xn)(x_{1}, \dots, x_{n}) coordinate system to (x1′,…,xn′)(x_{1}^{\prime}, \dots, x_{n}^{\prime}) coordinate system. x1′=f1(x1,…,xn)x2′=f2(x1,…,xn)⋮xn′=fn(x1,…,xn) \begin{align*} x_{1}^{\prime} &= f_{1}(x_{1}, \dots, x_{n}) \\ x_{2}^{\prime} &= f_{2}(x_{1}, \dots, x_{n}) \\ &\vdots \\ x_{n}^{\prime} &= f_{n}(x_{1}, \dots, x_{n}) \\ \end{align*}