c1537b1b-0995-44eb-9c29-f71f7c763c61 16 4 3 decimal

&[DATE] &[TIME] - &[FILENAME]

Quaternion rotation

ρ 1 b 2^- :

b 0.4 :

w ρ sqrt :

ρ 0.84

u v d b w b u * cosh (2^* b w v * sin * (2^+ (* :

u v f u - 2 ρ * b u * cosh * b u * sinh * u v d / + 2 w * b u * cosh * w v cos * w v * cos * - v sin w v * sin * - (* u v d / 2 w * b u * cosh * w v sin * w v * cos * - v cos w v * sin * - (* u v d / 31 mat :

M u v f 13.2 - 13.2 37.4 - 37.4 2020 CreateMesh :

α 0 :

β 0.00001 :

q 1 :

r 20 :

p 0.5 - :

a p q r - p 2^q 2^r 2^α p * β r * 033 mat :

The 'quat' is correct, the 'q' that feeds 'quat' is correct as well. However, Smath does not have Mathcad 11 Given/Find equivalent. Smath needs some dummy 'q,r', in fact, all parameters entering the solve block are fictious. For the given demo parameters [r quite large], the bidirectional rotation is obtained by 'b2 ±' only. 'p' has a magnifying and reversing effect. 1. Set dummy parameters. 2. Solve the system. 3. Create 'q' in two steps to feed 'quat'= γ 4. Plug γ in Andrey f(M,t)

b 05031 mat :

sol a 1 -^b * :

sol 0.5128 - 0 0.0128 31 mat

q sol p stack :

q 0.5128 - 0 0.0128 0.5 - 41 mat

b 01031 mat ≡ native unary-quaternion-rotation ≡

quat 12 q 3 el (2^* - 2 q 4 el (2^* - 2 q 2 el * q 3 el * 2 q 1 el * q 4 el * - 2 q 1 el * q 3 el * 2 q 2 el * q 4 el * + 2 q 1 el * q 4 el * 2 q 2 el * q 3 el * + 12 q 2 el (2^* - 2 q 4 el (2^* - 2 q 1 el * q 2 el * - 2 q 3 el * q 4 el * + 2 q 1 el * q 3 el * - 2 q 4 el * q 2 el * + 2 q 1 el * q 2 el * 2 q 3 el * q 4 el * + 12 q 2 el (2^* - 2 q 3 el (2^* - 33 mat :

q q q 2^sqrt / :

q q 2^sqrt /

γ quat :

Mathcad 11 'UnitVector' q/|q| has Smath equivalent

q 0.7159 - 0 0.0179 0.698 - 41 mat

γ 0.4997 0.5128 - 0.0131 - 0.5128 0.5 0.0128 - 0.0131 0.0128 - 0.9997 33 mat

M t f t B M γ * eval : t B 1 col t B 2 col augment 21 line :

step1 00 range :

c 00 + 200 red 15 mat :

Figure 2.5 4 Breather 14 black 15 mat :

M t f c Figure 3 1 sys