## RE: [Algorithms] dynamics in left-handed coordinate frames

 RE: [Algorithms] dynamics in left-handed coordinate frames From: Tom Forsyth - 2004-01-13 17:08:46 ```None of those change at all, except (1), where it will of course be "clockwise". Physics doesn't know or care what handedness your coordinate system is (except for a few funky little quantum effects). The only reasons "anti-clockwise" changes to "clockwise" is because our definition of those terms does not change with the handedness. If you instead talked about "the spin along the z axis from +ve x towards +ve y", then again, nothing changes. TomF. > -----Original Message----- > From: gdalgorithms-list-admin@... > [mailto:gdalgorithms-list-admin@...] On > Behalf Of Bob Dowland > Sent: 13 January 2004 16:39 > To: gdalgorithms-list@... > Subject: [Algorithms] dynamics in left-handed coordinate frames > > > A maths/dynamics question really for anyone who has tried > doing rigid body dynamics in a left handed world. I'm > wondering what or if there is a "usual" way to treat vector > x-products / Coriolis / and so on in a left handed coordinate system. > > For eg., in no particluar order, a RHS has: > > 1 angles increase anti-clockwise > > 2 e_i x e_j = e_k, for (i,j,k) any +ve perm of (1,2,3) > and e_i,j,k the usual unit direction vectors > > 3 Rdot = (omega*)R, ie epsilon_ijk.omega_j (R the > orientation of the body frame, omega the angular velocity > vector, epsilon_ijk the alternating tensor) > > 4 xdot_world = xdot_body + Cross(omega, x - cm_body) > > What happens to these in a LHS system to cope with > computation of angular quantities? > > Bob. ```

 [Algorithms] dynamics in left-handed coordinate frames From: Bob Dowland - 2004-01-13 16:39:15 ```A maths/dynamics question really for anyone who has tried doing rigid = body dynamics in a left handed world. I'm wondering what or if there is = a "usual" way to treat vector x-products / Coriolis / and so on in a = left handed coordinate system. For eg., in no particluar order, a RHS has: 1 angles increase anti-clockwise 2 e_i x e_j =3D e_k, for (i,j,k) any +ve perm of (1,2,3) and e_i,j,k the = usual unit direction vectors 3 Rdot =3D (omega*)R, ie epsilon_ijk.omega_j (R the orientation of the = body frame, omega the angular velocity vector, epsilon_ijk the = alternating tensor) 4 xdot_world =3D xdot_body + Cross(omega, x - cm_body) What happens to these in a LHS system to cope with computation of = angular quantities? Bob. ********************************************************************** The information contained in this email and its attachments is confidential. It is intended only for the named addressees=20 and may not be disclosed to anyone else without consent from Blue 52 Limited. Blue 52 gives no warranty that this email=20 message (including any attachments to it) is free of any virus=20 or other harmful matter and accepts no responsibility for any=20 loss or damage resulting from the recipient receiving, opening or using it.=20 ********************************************************************** ```
 RE: [Algorithms] dynamics in left-handed coordinate frames From: Tom Forsyth - 2004-01-13 17:08:46 ```None of those change at all, except (1), where it will of course be "clockwise". Physics doesn't know or care what handedness your coordinate system is (except for a few funky little quantum effects). The only reasons "anti-clockwise" changes to "clockwise" is because our definition of those terms does not change with the handedness. If you instead talked about "the spin along the z axis from +ve x towards +ve y", then again, nothing changes. TomF. > -----Original Message----- > From: gdalgorithms-list-admin@... > [mailto:gdalgorithms-list-admin@...] On > Behalf Of Bob Dowland > Sent: 13 January 2004 16:39 > To: gdalgorithms-list@... > Subject: [Algorithms] dynamics in left-handed coordinate frames > > > A maths/dynamics question really for anyone who has tried > doing rigid body dynamics in a left handed world. I'm > wondering what or if there is a "usual" way to treat vector > x-products / Coriolis / and so on in a left handed coordinate system. > > For eg., in no particluar order, a RHS has: > > 1 angles increase anti-clockwise > > 2 e_i x e_j = e_k, for (i,j,k) any +ve perm of (1,2,3) > and e_i,j,k the usual unit direction vectors > > 3 Rdot = (omega*)R, ie epsilon_ijk.omega_j (R the > orientation of the body frame, omega the angular velocity > vector, epsilon_ijk the alternating tensor) > > 4 xdot_world = xdot_body + Cross(omega, x - cm_body) > > What happens to these in a LHS system to cope with > computation of angular quantities? > > Bob. ```
 RE: [Algorithms] dynamics in left-handed coordinate frames From: Jon Watte - 2004-01-13 17:22:03 ```> A maths/dynamics question really for anyone who has tried doing > rigid body dynamics in a left handed world. I'm wondering what or > if there is a "usual" way to treat vector x-products / Coriolis / > and so on in a left handed coordinate system. Math is handed-less. X cross Y equals Z in RH and LH systems. Z, rotated +90 degrees about Y, yields X in RH and LH systems. The two worlds are the same; they're just mirrored. As long as you always use a consistent convention, the numbers are all the same. Note that the "change triangle winding" rule to do backface culling in LH vs RH come from "consistent convention": In a RH system, counter-clockwise is the same as RH spin around the angle going out of the screen; in a LH system, positive spin around the out-the-screen axis is clockwise. As long as you're careful about putting numbers in, and taking numbers out, using a consistent coordinate system, you'll be OK. This is no different from, say, matching units of force to units of mass, except it's a rather binary unit :-) Cheers, / h+ ```