ye shakhe az hendeseye na oghlidosye ke bishtar be kham haye kotahtarin zaman mesle charkhzad_cycloid_marbout mishe.masalan ma midonim ke tebgh ghazieh ye brachistochrone (!)to ye faza kootah tarin zaman momken baraye ye zare ke bekhad az a be b bere ye khat e rast nist balke ye charkhzade. moadeleh ash v_x =((dx)/(dt))-((d)/(dt))(sinθ)
=rω-r·((dsinθ)/(dθ))·((dθ)/(dt))=rω-rcosθω=rw(1-cosθ)=rω(1-cosωt):
v-y ham be hamin soorat dar miad =rωsinθ
dar paian bebakhshid ke inghadr bad neveshtam