All Questions
8 questions
4
votes
1
answer
145
views
Determining a direction/projection/heading for an object in 3D space after it has been rotated
I hope this is a good place to find an answer. Regardless, Worldbuilding looks like a great forum to follow.
I'm not a math wiz and I've tried to tackle this problem many times over the past decade or ...
- 51
-2
votes
1
answer
87
views
Why does the radius of curvature is constant in $n$-$t$ coordinate kinematics?
Deriving the relations kinematics on an $n$-$t$ coordinate system is said that if we have a particle $A$,after differential of time $dt$ the particle moves to $A'$. Assuming a curvilinear motion, the ...
-1
votes
2
answers
743
views
Derivative of transformation matrix for 6-DOF dynamics
I'm implementing a planner for a 6-DOF underwater robot and I'm using the dynamics derived in chapter 7.5 of Fossen's HHandbook of Marine Craft Hydrodynamics and Motion Control. I'm using the ...
- 1
1
vote
1
answer
153
views
Finding The Trajectory of particle Kept on a rotating surface
Suppose we "Keep" a particle on a circular, rotating turn-table, rotating with constant angular velocity $\dot{\theta}$, (i.e, the at $t=0$,when the particle makes contact with the table, the ...
- 1,325
0
votes
1
answer
819
views
What is the advantage of using a polar coordinate system with rotating unit vectors?
What is the advantage of using a polar coordinate system with rotating unit vectors? Kleppner's and Kolenkow's An Introduction to Mechanics states that base vectors $\mathbf{ \hat{r}}$ and $\mathbf{\...
- 307
0
votes
2
answers
258
views
Intuition for formula of tangential component of acceleration in general curvillinear motion
In certain problems of plane motion, the position of the particle P is
defined by its polar coordinates $r$ and $\theta$. It is then convenient to resolve the velocity and acceleration of the particle ...
- 551
1
vote
0
answers
86
views
Computing angular acceleration of a composition of coordinate frame transformations
Given two coordinate frames $A$ and $B$, we can define the transformation between them by:
$[\vec r_{AB}]_A$, the vector from the origin of $A$ to the origin of $B$ (resolved in frame $A$), and
$q_{...
- 633
2
votes
2
answers
997
views
At what point does force stop translating an object and start purely rotating it? [duplicate]
At what point (or distance) from the axis of rotation, does force applied on a rigid body stop translating and purely rotating the body? Can such a point even exist? Does the body always have to ...
- 500