Classification of integrable quadratic Hamiltonians on e(3)

Linear Poisson brackets on e(3) typical of rigid body dynamics are considered. All quadratic Hamiltonians of Kowalevski type having additional first integral of fourth degree are found. Quantum analogs of these Hamiltonians are listed.Comment: 11 page

Multi-Axis Solutions for MEMS Inertial Sensors

Inertial Measurement Unit (IMU) integrates three-axis gyroscopes and three-axis accelerometers to provide information about position, orientation, and trajectory. For decades, IMUs based on high-end sensors have been widely used for navigation, flight control, and stabilization functions. Inspired by recent improvements in performance of MEMS inertial sensors, this Ph.D. dissertation explores a large-scale integration of discrete inertial sensors in a single micro chip solution, and introduces two approaches for a compact tactical-grade MEMS IMU.The first approach is based on a silicon "origami-like" MEMS fabrication process, which involves fabrication of a high density array of discrete single-axis inertial sensors and then folding the array into a 3D IMU configuration. The main contribution of this thesis isinvention and implementation of a double-sided fabrication process for foldable structures with flexible polymer hinges, integrated high-end MEMS inertial sensors, and integration of thru-wafer interconnects in the fabrication process. Dissimilar materials were explored forfabrication of the "origami-like" structures, expanding our knowledge on the use of polymers and standard bulk and surface micro-machining tools for manufacturing of 3D MEMS devices. In addition, this work investigated two tactical-grade gyroscope designs for potential integration with the introduced fabrication process: Dynamically Amplified Gyroscope (DAG) and Toroidal Ring Gyroscope (TRG). We designed, modeled, and implemented the control electronics, and experimentally demonstrated the tactical-grade performance of the DAG and TRG gyroscopes. In this dissertation, for the first time, an IMU prototype with all sensors operational was reported, demonstrating feasibility of the Folded MEMS approach for implementation of a compact tactical-grade performance system.This thesis also explored a MEMS IMU solution, utilizing a single multi-axis sensing element. We demonstrated a 3-axis roll-pitch-yaw gyroscope, a major building block of the miniaturized IMU. The mechanical structure of the gyroscope employed a single vibrationalelement with a torsional drive mode and a multi-directional sense modes. Experimental characterization of the sensor showed that it is capable of measuring an angular rate around all three orthogonal axes simultaneously with a minimal cross talk betweenaxes of sensitivity and increased immunity to external vibrations

Multi-Axis Solutions for MEMS Inertial Sensors

Inertial Measurement Unit (IMU) integrates three-axis gyroscopes and three-axis accelerometers to provide information about position, orientation, and trajectory. For decades, IMUs based on high-end sensors have been widely used for navigation, flight control, and stabilization functions. Inspired by recent improvements in performance of MEMS inertial sensors, this Ph.D. dissertation explores a large-scale integration of discrete inertial sensors in a single micro chip solution, and introduces two approaches for a compact tactical-grade MEMS IMU.The first approach is based on a silicon "origami-like" MEMS fabrication process, which involves fabrication of a high density array of discrete single-axis inertial sensors and then folding the array into a 3D IMU configuration. The main contribution of this thesis isinvention and implementation of a double-sided fabrication process for foldable structures with flexible polymer hinges, integrated high-end MEMS inertial sensors, and integration of thru-wafer interconnects in the fabrication process. Dissimilar materials were explored forfabrication of the "origami-like" structures, expanding our knowledge on the use of polymers and standard bulk and surface micro-machining tools for manufacturing of 3D MEMS devices. In addition, this work investigated two tactical-grade gyroscope designs for potential integration with the introduced fabrication process: Dynamically Amplified Gyroscope (DAG) and Toroidal Ring Gyroscope (TRG). We designed, modeled, and implemented the control electronics, and experimentally demonstrated the tactical-grade performance of the DAG and TRG gyroscopes. In this dissertation, for the first time, an IMU prototype with all sensors operational was reported, demonstrating feasibility of the Folded MEMS approach for implementation of a compact tactical-grade performance system.This thesis also explored a MEMS IMU solution, utilizing a single multi-axis sensing element. We demonstrated a 3-axis roll-pitch-yaw gyroscope, a major building block of the miniaturized IMU. The mechanical structure of the gyroscope employed a single vibrationalelement with a torsional drive mode and a multi-directional sense modes. Experimental characterization of the sensor showed that it is capable of measuring an angular rate around all three orthogonal axes simultaneously with a minimal cross talk betweenaxes of sensitivity and increased immunity to external vibrations

On integrability of the Kontsevich nonabelian ODE system, accepted for publication

Abstract We consider systems of ODEs with the right hand side being Laurent polynomials in several non-commutative unknowns. In particular, these unknowns could be matrices of arbitrary size. An important example of such a system was proposed by M. Kontsevich. We prove the integrability of the Kontsevich system by finding a Lax pair, corresponding first integrals and commuting flows. We also provide a pre-Hamiltonian operator which maps gradients of integrals for the Kontsevich system to symmetries

Double-Sided Process for MEMS SOI Sensors with Deep Vertical Thru-Wafer Interconnects

This paper reports an approach for co-fabrication of silicon-on-insulator (SOI) sensors with low-resistance vertical electrical interconnects in thick (up to 600μm ) wafers. The thru-wafer interconnects double-sided (TWIDS) process is based on bottom-up seedless copper electroplating, and allows for voids-free features and high aspect ratio (wafer thickness to copper diameter ratio of 10:1). This work describes the design trade-offs, process flow, and characterization of interconnects. TWIDS technology is compatible with a standard SOI micro-electro-mechanical systems (MEMS) fabrication process and is applicable for micro sensors, such as accelerometers, gyroscopes, resonators, and RF MEMS devices, as well as for the 3-D MEMS assemblies. As a demonstration of potential applications, miniature toroidal ring gyroscopes were fabricated using the TWIDS process. The experimental characterization showed that the low-resistance interconnects with low parasitic losses are suitable for integration with capacitive-detection sensors. In addition, the mechanical stability of the interconnects is discussed in this paper, and a method to enhance structural rigidity by means of filling the insulating gaps with Parylene C is demonstrated. [2017-0179

Origami-Like 3-D Folded MEMS Approach for Miniature Inertial Measurement Unit

This paper presents a miniature 50 mm3 inertial measurement unit (IMU) implemented using a folded microelectromechanical systems (MEMS) process. The approach is based on wafer-level fabrication of high aspect-ratio single-axis sensors interconnected by flexible hinges and folded into a 3-D configuration, like a silicon Origami [1]. Two different materials for flexible hinges have been explored, including photo-definable polyimide and parylene-C. We report, for the first time, an IMU prototype with seven operational sensors: three accelerometers, three gyroscopes, and a prototype of a reference clock. This paper concludes with the results of experimental characterization of inertial sensors demonstrating the feasibility of the proposed approach for a compact IMU

Origami-Like 3-D Folded MEMS Approach for Miniature Inertial Measurement Unit

This paper presents a miniature 50 mm3 inertial measurement unit (IMU) implemented using a folded microelectromechanical systems (MEMS) process. The approach is based on wafer-level fabrication of high aspect-ratio single-axis sensors interconnected by flexible hinges and folded into a 3-D configuration, like a silicon Origami [1]. Two different materials for flexible hinges have been explored, including photo-definable polyimide and parylene-C. We report, for the first time, an IMU prototype with seven operational sensors: three accelerometers, three gyroscopes, and a prototype of a reference clock. This paper concludes with the results of experimental characterization of inertial sensors demonstrating the feasibility of the proposed approach for a compact IMU