According to the anti-phase sine current superposition theorem, the orientation, the magnetic flux density, the angular speed and the rotational direction of the spatial universal rotating magnetic field (SURMF) can...According to the anti-phase sine current superposition theorem, the orientation, the magnetic flux density, the angular speed and the rotational direction of the spatial universal rotating magnetic field (SURMF) can be controlled within the tri-axial orthogonal square Helmholtz coils (TOSHC). Nevertheless, three coupling direction angles of the normal vector of the SURMF in the Descartes coordinate system cannot be separately controlled, thus the adjustment of the orientation of the SURMF is difficult and the flexibility of the robotic posture control is restricted. For the dimension reduction and the decoupling of control variables, the orthogonal transformation operation theorem of the SURMF is proposed based on two independent rotation angular variables, which employs azimuth and altitude angles as two variables of the three-phase sine current superposition formula derived by the orthogonal rotation inverse transformation. Then the unique control rules of the orientation and the rotational direction of the SURMF are generalized in each spatial quadrant, thus the scanning of the normal vector of the SURMF along the horizontal or vertical direction can be achieved through changing only one variable, which simplifies the control process of the orientation of the SURMF greatly. To validate its feasibility and maneuverability, experiments were conducted in the animal intestine utilizing the innovative dual hemisphere capsule robot (DHCR) with active and passive modes. It was demonstrated that the posture adjustment and the steering rolling locomotion of the DHCR can be realized through single variable control, thus the orthogonal transformation operation theorem makes the control of the orientation of the SURMF convenient and flexible significantly. This breakthrough will lay a foundation for the human-machine interaction control of the SURMF.展开更多
This study extends the research on the self-consistent effective-one-body theory of a real spinless two-body system based on the post-Minkowskian approximation(Sci.China-Phys.Mech.Astron.65,100411(2022))to the case of...This study extends the research on the self-consistent effective-one-body theory of a real spinless two-body system based on the post-Minkowskian approximation(Sci.China-Phys.Mech.Astron.65,100411(2022))to the case of a binary system for the spinning black holes.An effective rotating metric and an improved Hamiltonian for the spinning black hole binaries are constructed.The decoupled equation for the null tetrad component of the gravitational perturbed Weyl tensorψ4B in the effective rotating spacetime is found with the help of the gauge transform characteristics of the Weyl tensors.The decoupled equation is then separated between radial and angular variables in the slowly rotating background spacetime,and a formal solution of ψ_(4)^(B) is obtained.On this basis,the formal expressions of the radiation reaction force and the waveform for the“plus”and“cross”modes of the gravitational wave are presented.These results,obtained in the same effective spacetime,constitute a self-consistent effective-one-body theory for the spinning black hole binaries based on the post-Minkowskian approximation.展开更多
基金supported by the National Natural Science Foundation of China (Grant Nos. 51277018, 61175102, & 51475115)the Open Fund of the State Key Laboratory of Mechanical Transmissions (Grant No.SKLMT-KFKT-201509)
文摘According to the anti-phase sine current superposition theorem, the orientation, the magnetic flux density, the angular speed and the rotational direction of the spatial universal rotating magnetic field (SURMF) can be controlled within the tri-axial orthogonal square Helmholtz coils (TOSHC). Nevertheless, three coupling direction angles of the normal vector of the SURMF in the Descartes coordinate system cannot be separately controlled, thus the adjustment of the orientation of the SURMF is difficult and the flexibility of the robotic posture control is restricted. For the dimension reduction and the decoupling of control variables, the orthogonal transformation operation theorem of the SURMF is proposed based on two independent rotation angular variables, which employs azimuth and altitude angles as two variables of the three-phase sine current superposition formula derived by the orthogonal rotation inverse transformation. Then the unique control rules of the orientation and the rotational direction of the SURMF are generalized in each spatial quadrant, thus the scanning of the normal vector of the SURMF along the horizontal or vertical direction can be achieved through changing only one variable, which simplifies the control process of the orientation of the SURMF greatly. To validate its feasibility and maneuverability, experiments were conducted in the animal intestine utilizing the innovative dual hemisphere capsule robot (DHCR) with active and passive modes. It was demonstrated that the posture adjustment and the steering rolling locomotion of the DHCR can be realized through single variable control, thus the orthogonal transformation operation theorem makes the control of the orientation of the SURMF convenient and flexible significantly. This breakthrough will lay a foundation for the human-machine interaction control of the SURMF.
基金supported by the National Natural Science Foundation of China(Grant Nos.12035005,and 12122504)the National Key Research and Development Program of China(Grant No.2020YFC2201400)。
文摘This study extends the research on the self-consistent effective-one-body theory of a real spinless two-body system based on the post-Minkowskian approximation(Sci.China-Phys.Mech.Astron.65,100411(2022))to the case of a binary system for the spinning black holes.An effective rotating metric and an improved Hamiltonian for the spinning black hole binaries are constructed.The decoupled equation for the null tetrad component of the gravitational perturbed Weyl tensorψ4B in the effective rotating spacetime is found with the help of the gauge transform characteristics of the Weyl tensors.The decoupled equation is then separated between radial and angular variables in the slowly rotating background spacetime,and a formal solution of ψ_(4)^(B) is obtained.On this basis,the formal expressions of the radiation reaction force and the waveform for the“plus”and“cross”modes of the gravitational wave are presented.These results,obtained in the same effective spacetime,constitute a self-consistent effective-one-body theory for the spinning black hole binaries based on the post-Minkowskian approximation.
