简介：mass-spring-damper-type的古典理论平常的扁平的空间3上的动态系统可以被reformulating概括到高度维的Riemannianmanifolds通过微分几何学的基本内在的物理原则。因为他们从当模特儿复杂物理结构自然地产生并且因为如此的动态系统为象信息的安全传播那样的几个现代应用程序组成基础，非线性的动态系统在科学文学被学习了。非线性的动态系统的流动可以在建筑群随着时间的过去演变，非重复(尽管确定)模式。现在的纸的焦点在提出描述在以一种没有坐标的方式歧管的Riemannian上滑动的一个点明智的粒子的动力学的一般方程上。纸显示出方程怎么在对科学文学的兴趣的某manifolds的情况中列举，例如歧管的Stiefel并且对称的积极明确的矩阵歧管。

简介：Anewresponse-spectrummodesuperpositionmethod,entirelyinrealvalueform,isdevelopedtoanalyzethemaximumstructuralresponseunderearthquakegroundmotionforgenerallydampedlinearsystemswithrepeatedeigenvaluesanddefectiveeigenvectors.Thisalgorithmhasclearphysicalconceptsandissimilartothecomplexcompletequadraticcombination(CCQC)methodpreviouslyestablished.Sinceitcanconsidertheeffectofrepeatedeigenvalues,itiscalledtheCCQC-Rmethod,inwhichthecorrelationcoefficientsofhigh-ordermodalresponsesareenclosedinadditiontothecorrelationcoefficientsinthenormalCCQCmethod.Asaresult,theformulasforcalculatingthecorrelationcoefficientsofhigh-ordermodalresponsesarededucedinthisstudy,includingdisplacement,velocityandvelocity-displacementcorrelationcoefficients.Furthermore,therelationshipbetweenhigh-orderdisplacementandvelocitycovarianceisderivedtomaketheCCQC-Ralgorithmonlyrelevanttothehigh-orderdisplacementresponsespectrum.Finally,apracticalstep-by-stepintegrationprocedureforcalculatinghigh-orderdisplacementresponsespectrumisobtainedbychangingtheearthquakegroundmotioninput,whichisevaluatedbycomparingittothetheorysolutionunderthesine-waveinput.Themethodderivedhereissuitableforgenerallylinearsystemswithclassicalornon-classicaldamping.