Perturbations of normal mode vibrations

A system consisting of two masses, interconnected by a coupling spring, and each connected to an anchor spring, is examined. The springs may be unequal and non-linear or even non-linearizable but each resists being compressed to the same degree as being stretched. Under the assumption that the system possesses a linear modal vibration, a theorem is established which guarantees that under small perturbations this periodic solution will be the generator of a continuous family of similar periodic solutions of the perturbed system. This theorem leads to a simple criterion which can readily be applied, for example, to a general homogeneous system.йccлeдyeтcя cиcтeмa cocтoящaя яз двyч мacc coeдииeнныч пpyзинoй й зaкpeплeниыч нa пpyзинaч. Пpyзины мoгyт быть нepoвными й нeлинeйными, йли дaзe нeлинeapизyeмыми,] oднaкo йч coпoтивлeниe cзaтиы paвнo coпpoтивлeниы pacтязeнйy. B пpeдпoлoзeнии нaличия линeйныч мoдeльныч кoлeбaний в cиcтeмe, дoкaзывaeтcя тeopeмa o гeнepиpoвaнии нeпpepывнoгo ceмeйcтвa пepиoдичecкич peшeний пoдoбныч мoдeльнoмy peщeниy, в cлyчae пoлoзeния нa нeгo мaлыч вoзмyщeний. Teopeмa дaeт яpocтoи кpитepий, qleгкo пpилoзимый, нaпpимep, к oбщим oднopoдным cиcтeмaм.