Recent content by WhiteFox

Ok, this clarifies a few things. First, for the sake of clarity for anyone who may be reading this, I'd like to point out that my original answer (and the original question) did not involve polar coordinates (which describe a point in terms of angle 'theta' and arc length 'r'). It was rather...

I'm not certain I understand your question. Maybe you could explain the context of your problem. Nonetheless, let me just say that expressing a force in terms of radial and tangential components only makes sense with respect to a specific point (i.e. the center of rotation). In other words...

Well, it's a matter of initial conditions: do you reach the speed prior to the first rain drops hitting you (in which case the only rain would be behind you and you would be dry) or do you reach the speed afterwards (in which case you would be surrounded be rain drops although there would be no...

Interesting problem. You might want to consider another vision of the same problem. Suppose that the box remains stationnary and that the velocity vector of the rain is equal to \vec{v}-\vec{u}. Also, instead of having to travel a distance L, suppose that the rain lasts for L/\|\vec{u}\|...

I would tend to think (i.e. I have no formal proof to provide at the moment) that your density 'rho' would depend on the walking speed (\vec{u}). For example, in an extreme case, consider that the speed vector of the rain \vec{v} is equal to your speed vector \vec{u} (on other words, raining...

Is the matrix you describe the projective space equivalent of the inertia tensor? If so, how would you go about applying rigid transformations (rotation & translation) using matrix multiplication? I tried the usual suspect (WMW^t) with your definition for M, with W = \left(...

Say f_x and f_y are your force components in cartesian coordinates (along x and y respectively), f_r is the radial component of the force and f_t is the tangential component of the force. And say that \theta is the angle of the line segment between the center of the circle and the point where...

I had loads of work to take care of, but I recently had time to take a closer at this problem. It is my current understanding that the authors of the paper use the quadrupole moment of mass distribution because it is a mathematical object easily converted to homogeneous coordinates, whereas I...

Actually, I'm not certain that the term 'mass tensor' is used by anyone else than the author of the aforementionned paper. As long as we are talking about the same mathematical object (and we are), I doesn't matter to me that it is not called 'mass tensor'. In fact, being a good scientist, I...

The vector has four components because it is in homogeneous coordinates. Homogeneous coordinates are often used in computer graphics and, as described in http://en.wikipedia.org/wiki/Homogeneous_coordinates" : The advantage in this case is that we can have a single transformation matrix 'W'...

If by \mathrm{d}^3 r you mean integration over the X, Y and Z axes, then indeed this is equivalent to the definition of mass tensor given by the author in her thesis: M = \int_V \rho(\vec{u}) \vec{u} \vec{u}^t \mathrm{d}x \mathrm{d}y \mathrm{d}z with \vec{u} = \left(...

...in more details... DOF stands for 'degree of freedom'. Loosly speaking, if a joint can rotate around or translate along one axis, it has 1 DOF. On the other hand, the shoulder allows rotation along all 3 axes and therefore represents 3 DOFs. In Lagrangian dynamics, (if I'm not mistaking)...

Hi, I'm a grad student in computer engineering and my research involves a fair amount of mechanics (forward/inverse dynamics). I'm working with rigid multibody systems with many DOFs (40 to 50) representing human characters. I've come across this...