graphics - How to draw multiple coordinates on mathematica?

For example:

How can I draw such kinds of coordinates?

Thank you~

Answer

You build this in Mathematica like you would do in any other descriptive language (you might want to use TikZ for this): step by step. Choosing nicer colors,adjusting the distances etc. is left as an exercise to the reader.

cosy[labels_, labelstyle_] := Flatten@{
    Arrow[{{0, 0, 0}, {1, 0, 0}}],
    Arrow[{{0, 0, 0}, {0, 1, 0}}],
    Arrow[{{0, 0, 0}, {0, 0, 1}}],
    labelstyle,
    Text[labels[[1]], {1.1, 0, 0}],
    Text[labels[[2]], {0, 1.1, 0}],
    Text[labels[[3]], {0, 0, 1.1}]
};

Graphics3D[{
    { (* Coordinate system 1 *)

   cosy[{"X", "Y", "Z"}, Darker@Orange],
        Darker@Orange,
        Text["World", {-.3, -.3, .5}]
    },
    { (* Coordinate system 2 *)

   Rotate[cosy[{"x", "y", "z"}, Blue], -30 \[Degree], {-1, 0, 1}]~

    Translate~{0, 0, -2}
    },

    { (* Connecting arrow *)
        Darker@Green,
        Arrow[{{0, 0, 0}, {0, 0, -2}}],
        Text["C(t)", {0, -.2, -1}]
    },

    { (* Red stuff *)

        Red,
        Arrow[{{0, 0, 0}, {0, 3, -1}}],
        Arrow[{{0, 0, -2}, {0, 3, -1}}],
        Text["\!\(\*SubscriptBox[\(p\), \(world\)]\)", 
    1/2 {0, 3, -1} + {0, 0, .5}],
        Text["\!\(\*SubscriptBox[\(p\), \(0\)]\)", 
    1/2 {0, 3, -1} + {0, 0, -1.5}],
        Text["p(t)", {0, 3, -1} + {0, .5, 0}]
    }
  }, Boxed -> False]