A vibrating structure gyroscope, defined by the IEEE as a Coriolis vibratory gyroscope (CVG), is a gyroscope that uses a vibrating structure to determine the rate of rotation. A vibrating structure gyroscope functions much like the halteres of flies (insects in the order Diptera). The underlying physical principle is that a vibrating object tends to continue vibrating in the same plane even if its support rotates. The Coriolis effect causes the object to exert a force on its support, and by measuring this force the rate of rotation can be determined. Vibrating structure gyroscopes are simpler and cheaper than conventional rotating gyroscopes of similar accuracy. Inexpensive vibrating structure gyroscopes manufactured with MEMS technology are widely used in smartphones, gaming devices, cameras and many other applications. Theory of operation Consider two proof masses vibrating in plane (as in the MEMS gyro) at frequency . The Coriolis effect induces an acceleration on the proof masses equal to , where is a velocity and is an angular rate of rotation. The in-plane velocity of the proof masses is given by , if the in-plane position is given by . The out-of-plane motion , induced by rotation, is given by: where is a mass of the proof mass, is a spring constant in the out of plane direction, is a magnitude of a rotation vector in the plane of and perpendicular to the driven proof mass motion. By measuring , we can thus determine the rate of rotation . Implementations Cylindrical resonator gyroscope (CRG) This type of gyroscope was developed by GEC Marconi and Ferranti in the 1980s using metal alloys with attached piezoelectric elements and a single-piece piezoceramic design. Subsequently, in the 90s, CRGs with magneto-electric excitation and readout were produced by American-based Inertial Engineering, Inc. in California, and piezo-ceramic variants by Watson Industries. A recently patented variant by Innalabs uses a cylindrical design resonator made from Elinvar-type alloy with piezoceramic elements for excitation and pickoff at its bottom. This breakthrough technology gave a substantially increased product life (MTBF > 500,000 hours); with its shock resistance (>300G), it should qualify for "tactical" (mid-accuracy) applications. The resonator is operated in its second-order resonant mode. The Q-factor is usually about 20,000; that pre-determines its noise and angular random walks. Standing waves are elliptically-shaped oscillations with four antinodes and four nodes located circumferentially along the rim. The angle between two adjacent antinode – nodes is 45