▁two - point - bound ary - value ▁optimal ▁control ▁problem ▁for ▁a ▁fixed ▁man eu ver ▁end ▁time . ▁Where as ▁an ▁eigen axis ▁man eu ver ▁maintain s ▁a ▁constant ▁rotation ▁axis ▁and ▁man eu ver ▁rate , ▁a ▁Z PM ▁uses ▁a ▁time ▁varying ▁rotation ▁axis ▁and ▁man eu ver ▁rate . ▁An ▁eigen axis ▁man eu ver ▁attitude ▁traject ory ▁tries ▁to ▁overcome ▁dist urban ces ▁to ▁maintain ▁a ▁constant ▁man eu ver ▁rate , ▁which ▁results ▁in ▁s atur ating ▁the ▁momentum ▁storage ▁devices . ▁By ▁using ▁a ▁variable ▁man eu ver ▁rate , ▁Z PM s ▁avoid ▁s atur ation ▁of ▁momentum ▁storage ▁actu ators . ▁ ▁A ▁simplified ▁model ▁for ▁a ▁space craft ▁Z PM ▁is ▁a ▁sail bo at . ▁A ▁sail bo at ▁tack s ▁against ▁the ▁wind ▁to ▁travel ▁in ▁a ▁z ig - z ag ▁manner ▁without ▁using ▁its ▁out board ▁mot ors ▁thus ▁not ▁using ▁any ▁prop ell ant . ▁The ▁sail bo at ▁takes ▁advantage ▁of ▁the ▁wind s ▁just ▁like ▁Z PM ▁takes ▁advantage ▁of ▁space craft ▁environmental ▁dist urban ces . ▁The ▁sail bo at ▁does ▁not ▁take ▁the ▁short est ▁path ▁to ▁travel ▁from ▁one ▁location ▁to ▁the ▁other . ▁Similarly , ▁a ▁Z PM ▁does ▁not ▁take ▁the ▁short est ▁angular ▁path ▁between ▁two ▁orient ations . ▁One ▁can ▁think ▁of ▁the ▁sail bo at ▁rud der ▁as ▁the ▁equivalent ▁of ▁the ▁momentum ▁storage ▁actu ators ▁on ▁a ▁space craft . ▁ ▁App lications ▁Z PM