(Two bivectors are equal when their parallelograms have equal areas and are in the same plane. That's where the redundancy comes in.)
On Sun, Jan 22, 2017 at 11:09 PM, Nick H <[email protected]> wrote: > In the same way that a vector is usually represented by a line segment, a > bivector can be represented by a parallelogram where the component vectors > form the sides. I was imagining a naive representation where you just store > the component vectors. > > type alias Bivector = { a : Vector, b : Vector } > > So if force and position are 3D vectors, then the torque bivector is 6D. > (But you could come up with more efficient representations that use fewer > components.) > > > > > > On Sun, Jan 22, 2017 at 5:58 PM, Max Goldstein <[email protected]> > wrote: > >> I think the quantities you meant to compare are torque and energy (both >>> of which have units of force*length). >>> >> >> Yup, sorry. >> >> >>> Torque, although sometimes expressed as a scalar or a vector, is >>> actually best represented as a bivector (two components per spatial >>> dimension in whatever system we are looking at). >>> >> >> How so? I know that the force and length are orthogonal, but that would >> still be one component per spatial dimension. >> >> -- >> You received this message because you are subscribed to the Google Groups >> "Elm Discuss" group. >> To unsubscribe from this group and stop receiving emails from it, send an >> email to [email protected]. >> For more options, visit https://groups.google.com/d/optout. >> > > -- You received this message because you are subscribed to the Google Groups "Elm Discuss" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. For more options, visit https://groups.google.com/d/optout.
