Question

how come a rigid body has six degrees of freedom?

Answer 1

Three translational coordinates and three euler angles specifying its orientation.

Answer 2

the degree of freedom (DOF) of a mechanical system is the number of independent parameters that define its configuration.

what about the velocities of atleast two points?

Answer 3

then that would mean 12 DOFs

Answer 4

wouldn't it?

Answer 5

No. The configuration (or arrangement) of a system requires the specification of the six parameters above. Velocity does not play a role.

Answer 6

Imagine a point mass travelling along a line -- it has a single degree of freedom, namely its coordinate along the line.

Answer 7

so DOFs don't give complete information about the body?

Answer 8

Nope.

Answer 9

Is there a particular reason you'd think they would?

Answer 10

i had always thought of DOFs as being parameters that completely define a state of an object.

Answer 11

At a particular moment of time, sure.

Answer 12

But the time evolution of the state requires more information.

Answer 13

okay.

Answer 14

More specifically, the state of the system (by which I mean its instantaneous configuration as well as its time evolution) is specified once you know all of the spatial parameters and their associated momenta.

Answer 15

Assuming you've studied intermediate mechanics to some degree, what you're thinking of is a point in phase space.

Answer 16

yes