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MacCullagh Ellipsoid
The MacCullagh ellipsoid is defined by the equation: :\frac + \frac + \frac = 2 E, where E is the energy and x,y,z are the components of the angular momentum, given in body's principal reference frame, with corresponding principal moments of inertia A,B,C. The construction of such ellipsoid was conceived by James MacCullagh.On the Rotation of a Solid Body round a Fixed Point; being an account of the late Professor Mac Cullagh's Lectures on that subject. Compiled by the Rev. Samuel Haughton, Fellow of Trinity College, Dublin. ransactions of the Royal Irish Academy, Vol. xxii. p. 139. Read April 23, 1849./ref> See also * Dzhanibekov effect * Poinsot's ellipsoid In classical mechanics, Poinsot's construction (after Louis Poinsot) is a geometrical method for visualizing the torque-free motion of a rotating rigid body, that is, the motion of a rigid body on which no external forces are acting. This motion ha ... References {{Reflist Rigid bodies ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Angular Momentum
Angular momentum (sometimes called moment of momentum or rotational momentum) is the rotational analog of Momentum, linear momentum. It is an important physical quantity because it is a Conservation law, conserved quantity – the total angular momentum of a closed system remains constant. Angular momentum has both a direction (geometry), direction and a magnitude, and both are conserved. Bicycle and motorcycle dynamics, Bicycles and motorcycles, flying discs, Rifling, rifled bullets, and gyroscopes owe their useful properties to conservation of angular momentum. Conservation of angular momentum is also why hurricanes form spirals and neutron stars have high rotational rates. In general, conservation limits the possible motion of a system, but it does not uniquely determine it. The three-dimensional angular momentum for a point particle is classically represented as a pseudovector , the cross product of the particle's position vector (relative to some origin) and its mo ... [...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] |
Ellipsoid
An ellipsoid is a surface that can be obtained from a sphere by deforming it by means of directional Scaling (geometry), scalings, or more generally, of an affine transformation. An ellipsoid is a quadric surface; that is, a Surface (mathematics), surface that may be defined as the zero set of a polynomial of degree two in three variables. Among quadric surfaces, an ellipsoid is characterized by either of the two following properties. Every planar Cross section (geometry), cross section is either an ellipse, or is empty, or is reduced to a single point (this explains the name, meaning "ellipse-like"). It is Bounded set, bounded, which means that it may be enclosed in a sufficiently large sphere. An ellipsoid has three pairwise perpendicular Rotational symmetry, axes of symmetry which intersect at a Central symmetry, center of symmetry, called the center of the ellipsoid. The line segments that are delimited on the axes of symmetry by the ellipsoid are called the ''principal ax ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
James MacCullagh
James MacCullagh (1809 – 24 October 1847) was an Irish mathematician and scientist. He served as the Erasmus Smith's Professor of Mathematics at Trinity College Dublin beginning in 1835, and in 1843, he was appointed as the Erasmus Smith's Professor of Natural and Experimental Philosophy. MacCullagh received the Cunningham Medal of the Royal Irish Academy in 1838 for his work on the laws of crystalline reflexion and light refraction, and the Copley Medal in 1842 for his efforts on the nature of light. Early life MacCullagh was born in Landahaussy, near Plumbridge, County Tyrone, Ireland, but the family moved to Curly Hill, Strabane when James was about 10. He was the eldest of twelve children and demonstrated mathematical talent at an early age. He entered Trinity College Dublin as a student in 1824, winning a scholarship in 1827 and graduating in 1829. Career He became a fellow of Trinity College Dublin in 1832 and was a contemporary there of William Rowan Hamilton. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tennis Racket Theorem
The tennis racket theorem or intermediate axis theorem, is a kinetic phenomenon of classical mechanics which describes the movement of a rigid body with three distinct principal moments of inertia. It has also been dubbed the Dzhanibekov effect, after Soviet Union, Soviet cosmonaut Vladimir Dzhanibekov, who noticed one of the theorem's logical consequences whilst in space in 1985. The effect was known for at least 150 years prior, having been described by Louis Poinsot in 1834 and included in standard physics textbooks such as Classical Mechanics (Goldstein), ''Classical Mechanics'' by Herbert Goldstein throughout the 20th century. The theorem describes the following effect: rotation of an object around its first and third Moment of inertia#Principal axes, principal axes is stable, whereas rotation around its second principal axis (or intermediate axis) is not. This can be demonstrated by the following experiment: Hold a tennis racket at its handle, with its face being horizo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Poinsot's Ellipsoid
In classical mechanics, Poinsot's construction (after Louis Poinsot) is a geometrical method for visualizing the torque-free motion of a rotating rigid body, that is, the motion of a rigid body on which no external forces are acting. This motion has four constants: the kinetic energy of the body and the three components of the angular momentum, expressed with respect to an inertial laboratory frame. The angular velocity vector \boldsymbol\omega of the rigid rotor is ''not constant'', but satisfies Euler's equations. The conservation of kinetic energy and angular momentum provide two constraints on the motion of \boldsymbol\omega. Without explicitly solving these equations, the motion \boldsymbol\omega can be described geometrically as follows: * The rigid body's motion is entirely determined by the motion of its inertia ellipsoid, which is rigidly fixed to the rigid body like a coordinate frame. * Its inertia ellipsoid rolls, without slipping, on the invariable plane, with the cen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
