Precession is a change in the orientation of the rotational axis of a rotating body. In an appropriate reference frame it can be defined as a change in the first Euler angle, whereas the third Euler angle defines the rotation itself. In other words, if the axis of rotation of a body is itself rotating about a second axis, that body is said to be precessing about the second axis. A motion in which the second Euler angle changes is called nutation. In physics, there are two types of precession: torque-free and torque-induced.
A gyroscope is a device used for measuring or maintaining orientation and angular velocity. It is a spinning wheel or disc in which the axis of rotation is free to assume any orientation by itself. When rotating, the orientation of this axis is unaffected by tilting or rotation of the mounting, according to the conservation of angular momentum.
The Foucault pendulum or Foucault's pendulum is a simple device named after French physicist Léon Foucault and conceived as an experiment to demonstrate the Earth's rotation. The pendulum was introduced in 1851 and was the first experiment to give simple, direct evidence of the earth's rotation. Today, Foucault pendulums are popular displays in science museums and universities.
A flywheel is a mechanical device specifically designed to efficiently store rotational energy. Flywheels resist changes in rotational speed by their moment of inertia. The amount of energy stored in a flywheel is proportional to the square of its rotational speed. The way to change a flywheel's stored energy is by increasing or decreasing its rotational speed by applying a torque aligned with its axis of symmetry,
The moment of inertia, otherwise known as the angular mass or rotational inertia, of a rigid body is a quantity that determines the torque needed for a desired angular acceleration about a rotational axis; similar to how mass determines the force needed for a desired acceleration. It depends on the body's mass distribution and the axis chosen, with larger moments requiring more torque to change the body's rotation rate. It is an extensive (additive) property: for a point mass the moment of inertia is just the mass times the square of the perpendicular distance to the rotation axis. The moment of inertia of a rigid composite system is the sum of the moments of inertia of its component subsystems. Its simplest definition is the second moment of mass with respect to distance from an axis. For bodies constrained to rotate in a plane, only their moment of inertia about an axis perpendicular to the plane, a scalar value, matters. For bodies free to rotate in three dimensions, their moments can be described by a symmetric 3 × 3 matrix, with a set of mutually perpendicular principal axes for which this matrix is diagonal and torques around the axes act independently of each other.
An electric unicycle is a self-balancing personal transporter with a single wheel. The rider controls the speed by leaning forwards or backwards, and steers by twisting the unit using their feet. The self-balancing mechanism uses gyroscopes and accelerometers in a similar way to that used by the Segway PT.
An inverted pendulum is a pendulum that has its center of mass above its pivot point. It is unstable and without additional help will fall over. It can be suspended stably in this inverted position by using a control system to monitor the angle of the pole and move the pivot point horizontally back under the center of mass when it starts to fall over, keeping it balanced. The inverted pendulum is a classic problem in dynamics and control theory and is used as a benchmark for testing control strategies. It is often implemented with the pivot point mounted on a cart that can move horizontally under control of an electronic servo system as shown in the photo; this is called a cart and pole apparatus. Most applications limit the pendulum to 1 degree of freedom by affixing the pole to an axis of rotation. Whereas a normal pendulum is stable when hanging downwards, an inverted pendulum is inherently unstable, and must be actively balanced in order to remain upright; this can be done either by applying a torque at the pivot point, by moving the pivot point horizontally as part of a feedback system, changing the rate of rotation of a mass mounted on the pendulum on an axis parallel to the pivot axis and thereby generating a net torque on the pendulum, or by oscillating the pivot point vertically. A simple demonstration of moving the pivot point in a feedback system is achieved by balancing an upturned broomstick on the end of one's finger.
A spinning top is a toy designed to spin rapidly on the ground, the motion of which causes it to remain precisely balanced on its tip due to its rotational inertia. Such toys have existed since antiquity. Traditionally tops were constructed of wood, sometimes with an iron tip, and would be set in motion by aid of a string or rope coiled around its axis which, when pulled quickly, caused a rapid unwinding that would set the top in motion. Today they are often built of plastic, and modern materials and manufacturing processes allow tops to be constructed with such precise balance that they can be set in motion by a simple twist of the fingers and twirl of the wrist without need for string or rope.
A gyrocar is a two-wheeled automobile. The difference between a bicycle or motorcycle and a gyrocar is that in a bike, dynamic balance is provided by the rider, and in some cases by the geometry and mass distribution of the bike itself, and the gyroscopic effects from the wheels. Steering a motorcycle is done by precessing the front wheel. In a gyrocar, balance was provided by one or more gyroscopes, and in one example, connected to two pendulums by a rack and pinion.
An escapement is a mechanical linkage in mechanical watches and clocks that gives impulses to the timekeeping element and periodically releases the gear train to move forward, advancing the clock's hands. The impulse action transfers energy to the clock's timekeeping element to replace the energy lost to friction during its cycle and keep the timekeeper oscillating. The escapement is driven by force from a coiled spring or a suspended weight, transmitted through the timepiece's gear train. Each swing of the pendulum or balance wheel releases a tooth of the escapement's escape wheel gear, allowing the clock's gear train to advance or "escape" by a fixed amount. This regular periodic advancement moves the clock's hands forward at a steady rate. At the same time the tooth gives the timekeeping element a push, before another tooth catches on the escapement's pallet, returning the escapement to its "locked" state. The sudden stopping of the escapement's tooth is what generates the characteristic "ticking" sound heard in operating mechanical clocks and watches. The first mechanical escapement, the verge escapement, was invented in medieval Europe during the 13th century, and was the crucial innovation which lead to the development of the mechanical clock. The design of the escapement has a large effect on a timepiece's accuracy, and improvements in escapement design drove improvements in time measurement during the era of mechanical timekeeping from the 13th through the 19th century.
A balance wheel, or balance, is the timekeeping device used in mechanical watches and some clocks, analogous to the pendulum in a pendulum clock. It is a weighted wheel that rotates back and forth, being returned toward its center position by a spiral torsion spring, the balance spring or hairspring. It is driven by the escapement, which transforms the rotating motion of the watch gear train into impulses delivered to the balance wheel. Each swing of the wheel allows the gear train to advance a set amount, moving the hands forward. The balance wheel and hairspring together form a harmonic oscillator, which due to resonance oscillates preferentially at a certain rate, its resonant frequency or 'beat', and resists oscillating at other rates. The combination of the mass of the balance wheel and the elasticity of the spring keep the time between each oscillation or ‘tick’ very constant, accounting for its nearly universal use as the timekeeper in mechanical watches to the present. From its invention in the 14th century until tuning fork and quartz movements became available in the 1960s, virtually every portable timekeeping device used some form of balance wheel.
In aeronautics, inertia coupling, also referred to as inertial coupling and inertial roll coupling, was a potentially catastrophic phenomenon of high-speed flight which caused the loss of aircraft and pilots before the design features to counter it, for example a big enough fin, were understood. It occurred when the inertia of a heavy fuselage exceeded the ability of the aerodynamic forces and moments generated by the wing and empennage to stabilize the aircraft. The problem became apparent as jet fighter aircraft and research aircraft were developed with narrow wingspans, that had relatively low roll inertia, caused by a long slender high-density fuselage, compared to the pitch and yaw inertias.
A torsion pendulum clock, more commonly known as an anniversary clock or 400-day clock, is a mechanical clock which keeps time with a mechanism called a torsion pendulum. This is a weighted disk or wheel, often a decorative wheel with 3 or 4 chrome balls on ornate spokes, suspended by a thin wire or ribbon called a torsion spring. The torsion pendulum rotates about the vertical axis of the wire, twisting it, instead of swinging like an ordinary pendulum. The force of the twisting torsion spring reverses the direction of rotation, so the torsion pendulum oscillates slowly, clockwise and counterclockwise. The clock's gears apply a pulse of torque to the top of the torsion spring with each rotation to keep the wheel going. The wheel and torsion spring function similarly to a watch's balance wheel and hairspring, as a harmonic oscillator to control the rate of the clock's hands.
A double inverted pendulum is the combination of the inverted pendulum and the double pendulum. The double inverted pendulum is unstable, meaning that it will fall down unless it is controlled in some way. The two main methods of controlling a double inverted pendulum are moving the base, as with the inverted pendulum, or by applying a torque at the pivot point between the two pendulums.
A PIGA is a type of accelerometer that can measure acceleration and simultaneously integrates this acceleration against time to produce a speed measure as well. The PIGA's main use is in Inertial Navigation Systems (INS) for guidance of aircraft and most particularly for ballistic missile guidance. It is valued for its extremely high sensitivity and accuracy in conjunction with operation over a wide acceleration range. The PIGA is still considered the premier instrument for strategic grade missile guidance, though systems based on MEMS technology are attractive for lower performance requirements.
The Furuta pendulum, or rotational inverted pendulum, consists of a driven arm which rotates in the horizontal plane and a pendulum attached to that arm which is free to rotate in the vertical plane. It was invented in 1992 at Tokyo Institute of Technology by Katsuhisa Furuta and his colleagues. It is an example of a complex nonlinear oscillator of interest in control system theory. The pendulum is underactuated and extremely non-linear due to the gravitational forces and the coupling arising from the Coriolis and centripetal forces. Since then, dozens, possibly hundreds of papers and theses have used the system to demonstrate linear and non-linear control laws. The system has also been the subject of two texts.
Ludwig Obry was an Austrian engineer and naval officer of the Austrian Navy who invented a gyroscopic device for steering a torpedo in 1895.
