In the mid-nineteenth century, Donders had proposed that for every human head rotating away from the primary pointing direction, the rotational vectors in the direction of the corresponding axes of rotation, is restri...In the mid-nineteenth century, Donders had proposed that for every human head rotating away from the primary pointing direction, the rotational vectors in the direction of the corresponding axes of rotation, is restricted to lie on a surface. Donders＇ intuition was that under such a restriction, the head orientation would be a function of its pointing direction. In this paper, we revisit Donders＇ Law and show that indeed the proposed intuition is true for a restricted class of head-orientations satisfying a class of quadratic Donders＇ surfaces, if the head points to a suitable neighborhood of the frontal pointing direction. Moreover, on a suitably chosen subspace of the 3D rotation group SO（3）, we describe a head movement dynamical system with input control signals that are the three external torques on the head provided by muscles. Three output signals are also suitably chosen as follows. Two of the output signals are coordinates of the frontal pointing direction. The third signal measures deviation of the state vector from the Donders＇ surface. We claim that the square system is locally feedback linearizable on the subspace chosen, and the linear dynamics is decomposed into parts, transverse and tangential to the Donders＇ surface. We demonstrate our approach by synthesizing a tracking and path-following controller. Additionally, for different choices of the Donders＇ surface parameters, head gaits are visualized by simulating different movement patterns of the head-top vector, as the head-pointing vector rotates around a circle.展开更多
The one-order phase of the echo changes if there is relative radial moving between the object and the radar, i.e. , the Doppler effect. The Doppler effect is widely used in radar signal processing. The transverse moti...The one-order phase of the echo changes if there is relative radial moving between the object and the radar, i.e. , the Doppler effect. The Doppler effect is widely used in radar signal processing. The transverse motion of the object cannot change the one-order phase of the echo, but the high-order phase. The high-order Doppler effect of the transverse moving target is presented and a new algorithm for obtaining the transverse velocity is given. The scalar velocity of a target moving steadily in any direction can be calculated with one-order and two-order items of the echo phase. The calculating method and simulating results are given. As the transverse speed is 900 km/h, the speed calculation error is less than 0. 06% if SNR of echo signal is higher than 0 dB.展开更多
We introduce a new class of partially coherent asymmetric array beams. When the beam propagates, the spectral density of each lobe and the corresponding degree of coherence have rotating behavior. Especially, not only...We introduce a new class of partially coherent asymmetric array beams. When the beam propagates, the spectral density of each lobe and the corresponding degree of coherence have rotating behavior. Especially, not only can array-like lattices revolve arbitrarily, but also they can move freely by controlling transverse plane shifts. Furthermore, we have generated this kind of beam experimentally, and the experimental phenomena are consistent with the numerical simulation results. Such a rotating beam with free movement and revolution may broaden the way for optical applications. More importantly, it inspires further studies in the field of asymmetric coherence gratings and lattices.展开更多
文摘In the mid-nineteenth century, Donders had proposed that for every human head rotating away from the primary pointing direction, the rotational vectors in the direction of the corresponding axes of rotation, is restricted to lie on a surface. Donders＇ intuition was that under such a restriction, the head orientation would be a function of its pointing direction. In this paper, we revisit Donders＇ Law and show that indeed the proposed intuition is true for a restricted class of head-orientations satisfying a class of quadratic Donders＇ surfaces, if the head points to a suitable neighborhood of the frontal pointing direction. Moreover, on a suitably chosen subspace of the 3D rotation group SO（3）, we describe a head movement dynamical system with input control signals that are the three external torques on the head provided by muscles. Three output signals are also suitably chosen as follows. Two of the output signals are coordinates of the frontal pointing direction. The third signal measures deviation of the state vector from the Donders＇ surface. We claim that the square system is locally feedback linearizable on the subspace chosen, and the linear dynamics is decomposed into parts, transverse and tangential to the Donders＇ surface. We demonstrate our approach by synthesizing a tracking and path-following controller. Additionally, for different choices of the Donders＇ surface parameters, head gaits are visualized by simulating different movement patterns of the head-top vector, as the head-pointing vector rotates around a circle.
基金Supported by the State Key Laboratory of Millimeter Waves(K200819)~~
文摘The one-order phase of the echo changes if there is relative radial moving between the object and the radar, i.e. , the Doppler effect. The Doppler effect is widely used in radar signal processing. The transverse motion of the object cannot change the one-order phase of the echo, but the high-order phase. The high-order Doppler effect of the transverse moving target is presented and a new algorithm for obtaining the transverse velocity is given. The scalar velocity of a target moving steadily in any direction can be calculated with one-order and two-order items of the echo phase. The calculating method and simulating results are given. As the transverse speed is 900 km/h, the speed calculation error is less than 0. 06% if SNR of echo signal is higher than 0 dB.
基金This work was supported by the National Natural Science Foundation of China(Nos.12174338 and 11874321)。
文摘We introduce a new class of partially coherent asymmetric array beams. When the beam propagates, the spectral density of each lobe and the corresponding degree of coherence have rotating behavior. Especially, not only can array-like lattices revolve arbitrarily, but also they can move freely by controlling transverse plane shifts. Furthermore, we have generated this kind of beam experimentally, and the experimental phenomena are consistent with the numerical simulation results. Such a rotating beam with free movement and revolution may broaden the way for optical applications. More importantly, it inspires further studies in the field of asymmetric coherence gratings and lattices.
