|
Inertia Coupling
In aeronautics, inertia coupling, also referred to as inertial coupling and inertial roll coupling, is a potentially catastrophic phenomenon of high-speed flight in a long, thin aircraft, in which an intentional rotation of the aircraft about one axis prevents the aircraft's design from inhibiting other unintended rotations. The problem became apparent in the 1950s, when the first supersonic jet fighter aircraft and research aircraft were developed with narrow wingspans, and caused the loss of aircraft and pilots before the design features to counter it (e.g. a big enough fin) were understood. The term "inertia/inertial coupling" has been criticized as misleading, because the phenomenon is not solely an instability of inertial movement, like the Janibekov effect. Instead, the phenomenon arises because aerodynamic forces react too slowly to track an aircraft's orientation. At low speeds and thick air, aerodynamic forces match aircraft translational velocity to orientation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
High-speed Flight
In high-speed flight, the assumptions of incompressibility of the air used in low-speed aerodynamics no longer apply. In subsonic aerodynamics, the theory of lift is based upon the forces generated on a body and a moving gas (air) in which it is immersed. At airspeeds below about , air can be considered incompressible in regards to an aircraft, in that, at a fixed altitude, its density remains nearly constant while its pressure varies. Under this assumption, air acts the same as water and is classified as a fluid. Subsonic aerodynamic theory also assumes the effects of viscosity (the property of a fluid that tends to prevent motion of one part of the fluid with respect to another) are negligible, and classifies air as an ideal fluid, conforming to the principles of ideal-fluid aerodynamics such as continuity, Bernoulli's principle, and circulation. In reality, air is compressible and viscous. While the effects of these properties are negligible at low speeds, compressibility ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mass Distribution
In physics and mechanics, mass distribution is the spatial distribution of mass within a solid body. In principle, it is relevant also for gases or liquids, but on Earth their mass distribution is almost homogeneous. Astronomy In astronomy mass distribution has decisive influence on the development e.g. of nebulae, stars and planets. The mass distribution of a solid defines its center of gravity and influences its dynamical behaviour - e.g. the oscillations and eventual rotation. Mathematical modelling A mass distribution can be modeled as a measure. This allows point masses, line masses, surface masses, as well as masses given by a volume density function. Alternatively the latter can be generalized to a distribution. For example, a point mass is represented by a delta function defined in 3-dimensional space. A surface mass on a surface given by the equation may be represented by a density distribution , where g/\left, \nabla f\ is the mass per unit area. The mathematical mo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Small Angle Approximation
For small angles, the trigonometric functions sine, cosine, and tangent can be calculated with reasonable accuracy by the following simple approximations: : \begin \sin \theta &\approx \tan \theta \approx \theta, \\[5mu] \cos \theta &\approx 1 - \tfrac12\theta^2 \approx 1, \end provided the angle is measured in radians. Angles measured in degree (angle), degrees must first be converted to radians by multiplying them by . These approximations have a wide range of uses in branches of physics and engineering, including mechanics, electromagnetics, electromagnetism, optics, cartography, astronomy, and computer science. One reason for this is that they can greatly simplify differential equations that do not need to be answered with absolute precision. There are a number of ways to demonstrate the validity of the small-angle approximations. The most direct method is to truncate the Maclaurin series for each of the trigonometric functions. Depending on the Order of approximation#Usag ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Space Shuttle
The Space Shuttle is a retired, partially reusable launch system, reusable low Earth orbital spacecraft system operated from 1981 to 2011 by the U.S. National Aeronautics and Space Administration (NASA) as part of the Space Shuttle program. Its official program name was the Space Transportation System (STS), taken from the 1969 plan led by U.S. vice president Spiro Agnew for a system of reusable spacecraft where it was the only item funded for development. The first (STS-1) of four orbital test flights occurred in 1981, leading to operational flights (STS-5) beginning in 1982. Five complete Space Shuttle orbiter vehicles were built and flown on a total of 135 missions from 1981 to 2011. They launched from the Kennedy Space Center (KSC) in Florida. Operational missions launched numerous satellites, interplanetary probes, and the Hubble Space Telescope (HST), conducted science experiments in orbit, participated in the Shuttle–Mir program, Shuttle-''Mir'' program with Russia, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Simple Harmonic Oscillator
In mechanics and physics, simple harmonic motion (sometimes abbreviated as ) is a special type of periodic function, periodic motion an object experiences by means of a restoring force whose magnitude is directly proportionality (mathematics), proportional to the distance of the object from an equilibrium position and acts towards the equilibrium position. It results in an oscillation that is described by a sinusoid which continues indefinitely (if uninhibited by friction or any other dissipation of energy). Simple harmonic motion can serve as a mathematical model for a variety of motions, but is typified by the oscillation of a mass on a spring (device), spring when it is subject to the linear elasticity (physics), elastic restoring force given by Hooke's law. The motion is sinusoidal in time and demonstrates a single resonance, resonant frequency. Other phenomena can be modeled by simple harmonic motion, including the motion of a pendulum, simple pendulum, although for it to b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
System Of Equations
In mathematics, a set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought. An equation system is usually classified in the same manner as single equations, namely as a: * System of linear equations, * System of nonlinear equations, * System of bilinear equations, * System of polynomial equations, * System of differential equations, or a * System of difference equations See also * Simultaneous equations model, a statistical model in the form of simultaneous linear equations * Elementary algebra Elementary algebra, also known as high school algebra or college algebra, encompasses the basic concepts of algebra. It is often contrasted with arithmetic: arithmetic deals with specified numbers, whilst algebra introduces variable (mathematics ..., for elementary methods {{set index article Equations Broad-concept articles de:Gleichung#Gleichungssysteme ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Time Derivative
A time derivative is a derivative of a function with respect to time, usually interpreted as the rate of change of the value of the function. The variable denoting time is usually written as t. Notation A variety of notations are used to denote the time derivative. In addition to the normal ( Leibniz's) notation, :\frac A very common short-hand notation used, especially in physics, is the 'over-dot'. I.E. :\dot (This is called Newton's notation) Higher time derivatives are also used: the second derivative with respect to time is written as :\frac with the corresponding shorthand of \ddot. As a generalization, the time derivative of a vector, say: : \mathbf v = \left v_1,\ v_2,\ v_3, \ldots \right is defined as the vector whose components are the derivatives of the components of the original vector. That is, : \frac = \left \frac,\frac ,\frac , \ldots \right . Use in physics Time derivatives are a key concept in physics. For example, for a changing position x, its ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Notation For Differentiation
In differential calculus, there is no single standard notation for differentiation. Instead, several notations for the derivative of a Function (mathematics), function or a dependent variable have been proposed by various mathematicians, including Gottfried Wilhelm Leibniz, Leibniz, Isaac Newton, Newton, Joseph Louis Lagrange, Lagrange, and Louis François Antoine Arbogast, Arbogast. The usefulness of each notation depends on the context in which it is used, and it is sometimes advantageous to use more than one notation in a given context. For more specialized settings—such as partial derivative, partial derivatives in multivariable calculus, tensor analysis, or vector calculus—other notations, such as subscript notation or the Nabla symbol, ∇ operator are common. The most common notations for differentiation (and its opposite operation, antiderivative, antidifferentiation or antiderivative, indefinite integration) are listed below. Leibniz's notation The original notati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Moment Of Inertia
The moment of inertia, otherwise known as the mass moment of inertia, angular/rotational mass, second moment of mass, or most accurately, rotational inertia, of a rigid body is defined relatively to a rotational axis. It is the ratio between the torque applied and the resulting angular acceleration about that axis. It plays the same role in rotational motion as mass does in linear motion. A body's moment of inertia about a particular axis depends both on the mass and its distribution relative to the axis, increasing with mass and distance from the axis. It is an intensive and extensive properties, extensive (additive) property: for a point particle, point mass the moment of inertia is simply the mass times the square of the perpendicular distance to the axis of rotation. The moment of inertia of a rigid composite system is the sum of the moments of inertia of its component subsystems (all taken about the same axis). Its simplest definition is the second Moment (physics), mome ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Control System
A control system manages, commands, directs, or regulates the behavior of other devices or systems using control loops. It can range from a single home heating controller using a thermostat controlling a domestic boiler to large industrial control systems which are used for controlling processes or machines. The control systems are designed via control engineering process. For continuously modulated control, a feedback controller is used to automatically control a process or operation. The control system compares the value or status of the process variable (PV) being controlled with the desired value or setpoint (SP), and applies the difference as a control signal to bring the process variable output of the plant to the same value as the setpoint. For sequential and combinational logic, software logic, such as in a programmable logic controller, is used. Open-loop and closed-loop control Feedback control systems Logic control Logic control systems for indus ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Angular Velocity
In physics, angular velocity (symbol or \vec, the lowercase Greek letter omega), also known as the angular frequency vector,(UP1) is a pseudovector representation of how the angular position or orientation of an object changes with time, i.e. how quickly an object rotates (spins or revolves) around an axis of rotation and how fast the axis itself changes direction. The magnitude of the pseudovector, \omega=\, \boldsymbol\, , represents the '' angular speed'' (or ''angular frequency''), the angular rate at which the object rotates (spins or revolves). The pseudovector direction \hat\boldsymbol=\boldsymbol/\omega is normal to the instantaneous plane of rotation or angular displacement. There are two types of angular velocity: * Orbital angular velocity refers to how fast a point object revolves about a fixed origin, i.e. the time rate of change of its angular position relative to the origin. * Spin angular velocity refers to how fast a rigid body rotates around a f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Euler's Equations (rigid Body Dynamics)
In classical mechanics, Euler's rotation equations are a vectorial quasilinear first-order ordinary differential equation describing the rotation of a rigid body, using a rotating reference frame with angular velocity ω whose axes are fixed to the body. They are named in honour of Leonhard Euler. In the absence of applied torques, one obtains the Euler top. When the torques are due to gravity, there are special cases when the motion of the top is integrable. Formulation Their general vector form is : \mathbf \dot + \boldsymbol\omega \times \left( \mathbf \boldsymbol\omega \right) = \mathbf. where ''M'' is the applied torques and ''I'' is the inertia matrix. The vector \dot is the angular acceleration. Again, note that all quantities are defined in the rotating reference frame. In orthogonal principal axes of inertia coordinates the equations become : \begin I_1\,\dot_ + (I_3-I_2)\,\omega_2\,\omega_3 &= M_\\ I_2\,\dot_ + (I_1-I_3)\,\omega_3\,\omega_1 &= M_\\ I_3\,\dot_ + ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
