简介：Inviewofdifferentialgeometry,thestatespaceofthermodynamicparametersisinvestigated.Herethegeometricalstructuresofthedenormalizedthermodynamicmanifoldareconsidered.Therelationoftheirgeometricalmetricsisobtained.Moreoveranexampleisusedtoillustrateourconclusions.

简介：我们证明那在那里存在位于一种保角的公制、兼容的连接形式，和公制的类型Hamiltonian下面与歧管(我们把它称为几何图画)，那能被放进与平常的Hamilton-Lagrange力学的通讯。二的动态等价的要求Hamiltonians打字，momenta由二幅图画产生了相等为乘都，是足够的决定保角的因素的扩大，在几何并列表示上定义，在它有到Hamiltonian-Lagrange图画的潜力的功能决定的所有订单的系数的analyticity的领域，在Hamilton-Lagrange并列表示，和它的衍生物上定义。相反地，如果保角的功能被知道，一幅Hamilton-Lagrange图画的潜力能以一个类似的方法被决定。我们证明在Hamilton-Lagrange图画的轨道的任意的本地变化能被变化在几何图画沿着geodesics产生并且建立为理解在几何图画的不稳定性怎么在不稳定性被表明提供一个基础的通讯原来的Hamiltonian运动。

简介：Nonlinearconsensusprotocolsfordynamicdirectednetworksofmulti-agentsystemswithfixedandswitchingtopologiesareinvestigatedseparatelyinthispaper.Basedonthecentremanifoldreductiontechnique,nonlinearconsensusprotocolsarepresented.Weprovethatagroupofagentscanreachaβ-consensus,thevalueofwhichisthegroupdecisionvaluevaryingfromtheminimumandthemaximumvaluesoftheinitialstatesoftheagents.Moreover,wederivetheconditionstoguaranteethatalltheagentsreachaβ-consensusonadesiredgroupdecisionvalue.Finally,asimulationstudyconcerningtheverticalalignmentmanoeuvereofateamofunmannedairvehiclesisperformed.Simulationresultsshowthatthenonlinearconsensusprotocolsproposedaremoreeffectivethanthelinearprotocolsfortheformationcontroloftheagentsandtheyareanimprovementoverexistingprotocols.