Various Coordinate Systems

from 東大1S力学A

• Various Coordinate Systems
  • Cartesian Coordinates
    • The vectors $\left(\begin{array}{c}1\\ 0\\ 0\end{array}\right),\left(\begin{array}{c}0\\ 1\\ 0\end{array}\right),\left(\begin{array}{c}0\\ 0\\ 1\end{array}\right)$ form a basis.
    • It is trivial that they are orthogonal to each other.
  • In Polar Coordinates, similar Basis Vectors can be defined.
    • It is difficult to grasp intuitively.
    • However, they still form an Orthogonal Basis (the basis vectors are orthogonal to each other).
  • Regardless of the chosen coordinate system, physics remains the same.
    • This is obvious, but it is important to note.
      • Therefore, it is recommended to choose a system that is convenient for the purpose.
      • It feels like advancing from high school physics (blu3mo)(blu3mo)
    • It is similar to how calculations are the same whether in Binary or Decimal (blu3mo)