Huygens synchronisation of three clocks equidistant from each other

In this paper we study the synchronisation of three identical oscillators, i.e., clocks, hanging from the same hard support. We consider the case where each clock interacts with the other two clocks. The synchronisation is attained through the exchange of small impacts between each pair of oscillators. The fundamental result of this article is that the final locked state is at phase difference of ((2{\pi})/3) from successive clocks (clockwise or counter-clockwise). Moreover, the locked states attract a set whose closure is the global set of initial conditions. The methodology of our analysis consists in the construction a model, which is a non-linear discrete dynamical system, i.e. a non-linear difference equation. The results are extendable to any set of three oscillators under mutual symmetric interaction, despite the particular models of the oscillators

Japan: A Normal State?

This article seeks to demonstrate that Japan throughout time has made gradual adjustmentsthroughout time to increase its military capacities, in order to regain autonomy in relation toits defence. With this process of “adjustment”, without constitutional reforms, Japan presentlypossesses military capabilities that are similar to those of the primary global powers in termsof budget, technologically advanced military resources, manpower, and it masters the entirecycle for the production of a nuclear weapon. In an unstable regional scenario, entwinedwith the rise of threat to Japan’s strategic and economic security and with the increase of thepossibility of being abandoned by the United States, what is preventing Japan in claimingits defence autonomy and taking collective security actions? The first part of this reflectionintroduces some concepts that indicate the contradictions, paradoxes, and fundaments thatunderpin the construction of the Japanese security identity. The second part concentrates onthe analysis of the tendency of revision or of reinterpretation of the Japanese Constitutionwith regards to possessing Armed Forces as a foreign policy instrument.Este artigo propõe demonstrar que o Japão aplicou ao longo do tempo ajustes graduais decrescimento das suas capacidades militares para recuperar autonomia em sua própria defesa.Com este processo de “ajustes”, sem reformas constitucionais, Japão detém atualmentecapacidades militares similares às das principais potências mundiais em termos de orçamento,recursos materiais tecnologicamente avançados, contingentes humanos e domina todos os ciclos para produção da arma nuclear. Em um cenário regional instável, com a emergênciade riscos à sua segurança estratégica e econômica e com aumento da possibilidade de serabandonado pelos Estados Unidos, o que falta para o Japão assumir sua autonomia em defesae atuar em ações de segurança coletiva? O texto avalia, na primeira parte, alguns conceitosque apontam as contradições, paradoxos e fundamentos que embasam a construção daidentidade de segurança do Japão. E, na segunda, concentra-se na análise da tendência derevisão ou de reinterpretação da Constituição Japonesa no que tange ter Forças Armadascomo instrumentos de Política Externa