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Motion laws.

See File:Cinematique croix malte relation angles.svg

τ = (2α - π)/ω

For 0 < t < τ

${\displaystyle \tan \theta _{\mathrm {s} }={\frac {\sin \theta _{\mathrm {e} }}{k-\cos \theta _{\mathrm {e} }}}}$

${\displaystyle \theta _{\mathrm {s} }=\operatorname {arctan} \left({\frac {\sin \theta _{\mathrm {e} }}{k-\cos \theta _{\mathrm {e} }}}\right)}$

${\displaystyle \omega _{\mathrm {s} }={\dot {\theta }}_{\mathrm {s} }={\frac {\omega (k\cos \theta _{\mathrm {e} }-1)}{k^{2}-2k\cos \theta _{\mathrm {e} }+1}}}$

${\displaystyle \alpha _{\mathrm {s} }={\ddot {\theta }}_{\mathrm {s} }={\frac {\omega ^{2}(k^{2}-1)\sin \theta _{\mathrm {e} }}{(k^{2}-2k\cos \theta _{\mathrm {e} }+1)^{2}}}}$.

${\displaystyle j_{\mathrm {a} }={\frac {\mathrm {d} ^{3}\theta _{\mathrm {s} }}{\mathrm {d} t^{3}}}\ ={\frac {\omega ^{3}(k^{2}-1)}{(k^{2}-2k\cos \theta _{\mathrm {e} }+1)^{3}}}(2k\cos ^{2}\theta _{\mathrm {e} }+(k^{2}+1)\cos \theta _{\mathrm {e} }-4k)}$

Scilab source.

See File:Chronogrammes croix malte 4 branches.svg

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