- #1

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## Main Question or Discussion Point

We know that energy is a function of space and velocity and it’s constant (in ideal case) though time.

So ## E(\vec{x}(t) , \vec{\dot{x}}(t)) = E_0##

where ##\vec{x} , \vec{\dot{x}} \in \mathbb{R}^3##.

So my function is ##E : \mathbb{R}^6 \rightarrow \mathbb{R}##.

Then there is my question: my teacher said that the motion will not be in a 6-dimensional space but on a 5-dimensional *surface*.

I don’t understand that statement (and maybe I understood it wrongly).

Anybody can help me?

So ## E(\vec{x}(t) , \vec{\dot{x}}(t)) = E_0##

where ##\vec{x} , \vec{\dot{x}} \in \mathbb{R}^3##.

So my function is ##E : \mathbb{R}^6 \rightarrow \mathbb{R}##.

Then there is my question: my teacher said that the motion will not be in a 6-dimensional space but on a 5-dimensional *surface*.

I don’t understand that statement (and maybe I understood it wrongly).

Anybody can help me?