Following the basic principles stated by Painlevé, we first revisit the process of selecting the admissible time-independent Hamiltonians H = （p1^2 ＋ p2^2）/2 ＋ V（q1, q2） whose some integer power qj^nj （t）...Following the basic principles stated by Painlevé, we first revisit the process of selecting the admissible time-independent Hamiltonians H = （p1^2 ＋ p2^2）/2 ＋ V（q1, q2） whose some integer power qj^nj （t） of the general solution is a singlevalued function of the complez time t. In addition to the well known rational potentials V of Hénon-Heiles, this selects possible cases with a trigonometric dependence of V on qj. Then, by establishing the relevant confluences, we restrict the question of the explicit integration of the seven （three “cubic” plus four “quartic”） rational Hénon-Heiles cases to the quartic cases. Finally, we perform the explicit integration of the quartic cases, thus proving that the seven rational cases have a meromorphic general solution explicitly given by a genus two hyperelliptic function.展开更多
The cylindrical worm processed by annular grinding wheel envelope in two degree of freedom motion state is a novel worm. This paper explains the shaping principle of such a worm. To improve meshing quality and the p...The cylindrical worm processed by annular grinding wheel envelope in two degree of freedom motion state is a novel worm. This paper explains the shaping principle of such a worm. To improve meshing quality and the properties of contact and lubrication, the multi objective optimization has been conducted for the first time to the parameters of such a worm pair by the fuzzy optimal method. The results show that, the shape of the contact line is visibly more sloped than before being optimized, lubrication angle is apparently bigger, and the distribution of contact lines is much improved.展开更多
文摘Following the basic principles stated by Painlevé, we first revisit the process of selecting the admissible time-independent Hamiltonians H = （p1^2 ＋ p2^2）/2 ＋ V（q1, q2） whose some integer power qj^nj （t） of the general solution is a singlevalued function of the complez time t. In addition to the well known rational potentials V of Hénon-Heiles, this selects possible cases with a trigonometric dependence of V on qj. Then, by establishing the relevant confluences, we restrict the question of the explicit integration of the seven （three “cubic” plus four “quartic”） rational Hénon-Heiles cases to the quartic cases. Finally, we perform the explicit integration of the quartic cases, thus proving that the seven rational cases have a meromorphic general solution explicitly given by a genus two hyperelliptic function.
文摘The cylindrical worm processed by annular grinding wheel envelope in two degree of freedom motion state is a novel worm. This paper explains the shaping principle of such a worm. To improve meshing quality and the properties of contact and lubrication, the multi objective optimization has been conducted for the first time to the parameters of such a worm pair by the fuzzy optimal method. The results show that, the shape of the contact line is visibly more sloped than before being optimized, lubrication angle is apparently bigger, and the distribution of contact lines is much improved.
