2 math foramting a bit of rewording

I'm solving fortrying to obtain the dynamic model of a 3D robot (academic problem), I have obtained the D-H table, the transformation matrix for each pair of links and the total transformation matrix. Now I'm struggling with the computing ofthe total Kinetic energy (for using it in the lagrangianLagrangian approach).

In some texts, it is shown the using of only the linear velocity is used in the computing ofthe kinetic energy, even if there are revolute links, that is: K=(1/2)m*|v|^2

$$K=\frac{1}{2}m~v^2$$

But in some others, it is shownboth the using of alsolinear and the angular velocity with the Inertia tensor: K=(1/2)m*|v|^2 +velocities are considered (1/2)I*|w|^2:

$$K=\frac{1}{2}m~v^2 + \frac{1}{2} I~\omega^2$$

I'm a little bit confused with this, when and when not to use the Inertia tensor inangular contribution to the computing of Kinetic energy?

Thank you and sorry for my bad english.

I'm solving for the dynamic model of a 3D robot (academic problem), I have obtained the D-H table, the transformation matrix for each pair of links and the total transformation matrix. Now I'm struggling with the computing of Kinetic energy (for using it in the lagrangian approach).

In some texts, it is shown the using of only the linear velocity in the computing of kinetic energy, even if there are revolute links, that is: K=(1/2)m*|v|^2

But in some others, it is shown the using of also the angular velocity with the Inertia tensor: K=(1/2)m*|v|^2 + (1/2)I*|w|^2

I'm a little bit confused with this, when and when not to use the Inertia tensor in the computing of Kinetic energy?

Thank you and sorry for my bad english.

I'm trying to obtain the dynamic model of a 3D robot (academic problem), I have obtained the D-H table, the transformation matrix for each pair of links and the total transformation matrix. Now I'm struggling with computing the total Kinetic energy (for using it in the Lagrangian approach).

In some texts, only the linear velocity is used in computing the kinetic energy, even if there are revolute links, that is:

$$K=\frac{1}{2}m~v^2$$

But in some others, both the linear and the angular velocities are considered :

$$K=\frac{1}{2}m~v^2 + \frac{1}{2} I~\omega^2$$

I'm a little bit confused with this, when and when not to use the angular contribution to the Kinetic energy?

1

# When and when not to use the Inertia tensor in Kinetic energy computing?

I'm solving for the dynamic model of a 3D robot (academic problem), I have obtained the D-H table, the transformation matrix for each pair of links and the total transformation matrix. Now I'm struggling with the computing of Kinetic energy (for using it in the lagrangian approach).

In some texts, it is shown the using of only the linear velocity in the computing of kinetic energy, even if there are revolute links, that is: K=(1/2)m*|v|^2

But in some others, it is shown the using of also the angular velocity with the Inertia tensor: K=(1/2)m*|v|^2 + (1/2)I*|w|^2

I'm a little bit confused with this, when and when not to use the Inertia tensor in the computing of Kinetic energy?

Thank you and sorry for my bad english.