The wobbling excitations of the triaxial superdeformed (TSD) bands in the Lu and Hf region are studied by the microscopic framework of the cranked mean-field and the randomphase approximation (RPA). In contrast to the previous works, where the Nilsson potential was used, the more realistic Woods-Saxon potential is employed as a nuclear mean-field. It is pointed out that the original formulation should be slightly modified for general meanfield like the Woods-Saxon potential. The wobbling-like RPA solutions have been found systematically in the nuclei studied and their characteristic properties are investigated in detail. This confirms the wobbling phonon excitations in TSD nuclei from the microscopic calculations. The result of B(E2) values indicates that the triaxial deformation is increasing as a function of spin in the observed TSD bands in 163 Lu.Subject Index: 210, 211, 212 §1. IntroductionThe observation of the wobbling excitations 1), 2) (see also Refs. 3) and 4)) renewed the interest in the study of nuclear rotational motions. The nuclear wobbling motion 5) is a quantized motion of the triaxial rotor and appears as a multiple-band structure, in which consecutive rotational bands are connected by strong E2 transitions with each other. Until now, the multiple rotational band structure characteristic to the wobbling phonon excitation has been observed at the high-spin excited states in some Lu isotopes 1)-3), 6)-10) around 163 Lu. Nuclei in the Lu and Hf region, including these Lu isotopes, have been predicted to be strongly deformed with pronounced triaxiality 11)-14) at high-spin states, and the associated rotational bands are called triaxial superdeformed (TSD) bands; i.e., the wobbling structure is composed of these TSD bands. In fact the lifetime measurements in these nuclei 15), 16) revealed that the rotational E2 transition probabilities inside the bands are typically about 500 Weisskopf units, and those between the bands associated with the wobbling phonon excitations are about 100 Weisskopf units. These are one of the largest out-of-band B(E2) and believed to be the evidence of the nuclear wobbling motion. Although several candidates of the TSD bands have been observed in even-even Hf isotopes, 17)-21) there is no definite evidence of the wobbling excitation yet.The nuclear wobbling motion was first predicted by using the simple macroscopic rotor model. 5) The experimental data observed in Lu isotopes are investigated by the particle-rotor model, 22)-25) because a i 13/2 quasiproton exists in the proton-odd Lu nuclei. It is, however, noted that the properties of the observed out-of-band E2 transitions suggest that the triaxial deformation is of the so-called positive-γ by guest on April 13, 2015 http://ptp.oxfordjournals.org/ Downloaded from T. Shoji and Y. R. Shimizu shape in the Lund convention, 26) the sign of which is opposite to that of Ref. 5); namely the moment of inertia about the shortest axis of triaxial deformation is the largest. This conflicts with the irrotational moments of inertia wh...

There are various different definitions for the triaxial deformation parameter "γ ". It is pointed out that the parameter conventionally used in the Nilsson (or Woods-Saxon) potential, γ (pot:Nils) [or γ (pot:WS)], is not appropriate for representing the triaxiality γ defined in terms of the intrinsic quadrupole moments. The difference between the two can be as large as a factor two in the case of the triaxial superdeformed bands recently observed in Hf and Lu nuclei, i.e., γ (pot:Nils) ≈ 20 • corresponds to γ ≈ 10 • . In our previous work, we studied the wobbling excitations in Lu nuclei using the microscopic framework of the cranked Nilsson mean-field and the random phase approximation. The most serious problem was that the calculated B(E2) value is about factor two too small. It is shown that the origin of this underestimate can mainly be attributed to the small triaxial deformation parameter γ ≈ 10 • that corresponds to γ (pot:Nils) ≈ 20 • . If the same triaxial deformation parameter is used as in the analysis of the particle-rotor model, γ ≈ 20 • , the calculated B(E2) gives correct magnitude of the experimental data.

The nuclear wobbling motion in the Lu region is studied by the microscopic cranked mean-field plus RPA method. The Woods-Saxon potential is used as a mean-field with a new parameterization which gives reliable description of rapidly rotating nuclei. The prescription of symmetry-preserving residual interaction makes the calculation of the RPA step parameter-free, and we find the wobbling-like RPA solution if the triaxial deformation of the mean-field is suitably chosen. It is shown that the calculated outof-band B(E2) of the wobbling-like solution depends on the triaxial deformation in the same way as in the macroscopic rotor model, and can be used to probe the triaxiality of the nuclear mean-field.where the wobbling energy ω wob is given byHere it is assumed that the main rotation axis is the x-axis (J x > J y , J z ). This type of rotational motion is only possible when the system is triaxially deformed, and appears as a multiple band structure shown in Fig. 1. It is composed of a

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Abstract-This paper deals with motion control of throwing generated by dexterous action. Dexterous actions can be seen in many sports. In baseball pitching, dexterous throwing seems to use energy transfer and a physical constraint at the elbow joint. To implement the dexterous throwing, two types of twolink underactuated manipulator are presented. One model has a spring at 2nd joint which represents an arm's stiffness and a constraint at elbow joint, another model has a physical absolute constraint at elbow joint. For these models, throwing motion control method based on output zeroing which specifies the path of the ball held by an end-effector is proposed. The proposed control strategy realizes the energy efficient motion for throwing to the desired direction. Simulation and experimental results show the effectiveness of the proposed control method.

This brief describes a control strategy for the throwing motion of an underactuated two-link planar robot called the Pendubot. The springed Pendubot is built based on the concept of unstable zero dynamics, and our investigation uses it as a dynamic model of superior limbs to imitate human throwing motion. In the proposed control strategy, the zero dynamics is intentionally destabilized when a ball held by the end-effector is constrained on a geometric path in a vertical plane, using output zeroing control for the deviation between the ball and geometric path. The unstable zero dynamics drives the ball along the geometric path to achieve fast and accurate throw in a desired direction. The unstable zero dynamics is analytically derived to guarantee the dynamic acceleration of the ball along the geometric path. Numerical simulations and experimental results confirm the effectiveness of the proposed control strategy.

Abstract-This paper presents systematic methods for throwing motion control of the Pendubot based on the concept of explosively unstable zero dynamics. The Pendubot, an underactuated two-link planar robot, is investigated as a dynamic model of the superior limbs for imitation of human throwing motion whose models are fundamentally underactuated in nature. The controller is designed based on input-output linearization and output zeroing control since the Pendubot is not input-state linearizable. The originality of this paper is to intentionally destabilize the zero dynamics, a nonlinear dynamics which remains unobservable from the output when the partially linearized dynamics converges exponentially to zero, to generate dynamic acceleration of the ball. Mathematical analysis of ordinary differential equations guarantees the explosive instability of the zero dynamics. Numerical simulations verify the effectiveness of the proposed control strategy.

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