(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 <falling.maso...@gmail.com> 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 <maxgoldste...@gmail.com>
> 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.
>>
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