Newton's cannonballNewton's cannonball was a thought experiment Isaac Newton used to hypothesize that the force of gravity was universal, and it was the key force for planetary motion. It appeared in his posthumously published 1728 work De mundi systemate (also published in English as A Treatise of the System of the World). Newton's original plan for Philosophiæ Naturalis Principia Mathematica was that it should consist of two books, the first analyzing basic laws of motion, and the second applying them to the Solar System.
Euler's laws of motionIn classical mechanics, Euler's laws of motion are equations of motion which extend Newton's laws of motion for point particle to rigid body motion. They were formulated by Leonhard Euler about 50 years after Isaac Newton formulated his laws. Euler's first law states that the rate of change of linear momentum p of a rigid body is equal to the resultant of all the external forces Fext acting on the body: Internal forces between the particles that make up a body do not contribute to changing the momentum of the body as there is an equal and opposite force resulting in no net effect.
Differential geometryDifferential geometry is a mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It uses the techniques of differential calculus, integral calculus, linear algebra and multilinear algebra. The field has its origins in the study of spherical geometry as far back as antiquity. It also relates to astronomy, the geodesy of the Earth, and later the study of hyperbolic geometry by Lobachevsky.
Differential (mathematics)In mathematics, differential refers to several related notions derived from the early days of calculus, put on a rigorous footing, such as infinitesimal differences and the derivatives of functions. The term is used in various branches of mathematics such as calculus, differential geometry, algebraic geometry and algebraic topology. The term differential is used nonrigorously in calculus to refer to an infinitesimal ("infinitely small") change in some varying quantity.
Lift-to-drag ratioIn aerodynamics, the lift-to-drag ratio (or L/D ratio) is the lift generated by an aerodynamic body such as an aerofoil or aircraft, divided by the aerodynamic drag caused by moving through air. It describes the aerodynamic efficiency under given flight conditions. The L/D ratio for any given body will vary according to these flight conditions. For an aerofoil wing or powered aircraft, the L/D is specified when in straight and level flight. For a glider it determines the glide ratio, of distance travelled against loss of height.
Kepler's laws of planetary motionIn astronomy, Kepler's laws of planetary motion, published by Johannes Kepler between 1609 and 1619, describe the orbits of planets around the Sun. The laws modified the heliocentric theory of Nicolaus Copernicus, replacing its circular orbits and epicycles with elliptical trajectories, and explaining how planetary velocities vary. The three laws state that: The orbit of a planet is an ellipse with the Sun at one of the two foci. A line segment joining a planet and the Sun sweeps out equal areas during equal intervals of time.
Gauss's law for gravityIn physics, Gauss's law for gravity, also known as Gauss's flux theorem for gravity, is a law of physics that is equivalent to Newton's law of universal gravitation. It is named after Carl Friedrich Gauss. It states that the flux (surface integral) of the gravitational field over any closed surface is proportional to the mass enclosed. Gauss's law for gravity is often more convenient to work from than Newton's law. The form of Gauss's law for gravity is mathematically similar to Gauss's law for electrostatics, one of Maxwell's equations.
Differential of a functionIn calculus, the differential represents the principal part of the change in a function with respect to changes in the independent variable. The differential is defined by where is the derivative of f with respect to , and is an additional real variable (so that is a function of and ). The notation is such that the equation holds, where the derivative is represented in the Leibniz notation , and this is consistent with regarding the derivative as the quotient of the differentials.
RotationRotation or rotational motion is the circular movement of an object around a central line, known as axis of rotation. A plane figure can rotate in either a clockwise or counterclockwise sense around a perpendicular axis intersecting anywhere inside or outside the figure at a center of rotation. A solid figure has an infinite number of possible axes and angles of rotation, including chaotic rotation (between arbitrary orientations), in contrast to rotation around a axis.
Magnetic confinement fusionMagnetic confinement fusion is an approach to generate thermonuclear fusion power that uses magnetic fields to confine fusion fuel in the form of a plasma. Magnetic confinement is one of two major branches of fusion energy research, along with inertial confinement fusion. The magnetic approach began in the 1940s and absorbed the majority of subsequent development. Fusion reactions combine light atomic nuclei such as hydrogen to form heavier ones such as helium, producing energy.
Solid modelingSolid modeling (or solid modelling) is a consistent set of principles for mathematical and computer modeling of three-dimensional shapes (solids). Solid modeling is distinguished within the broader related areas of geometric modeling and computer graphics, such as 3D modeling, by its emphasis on physical fidelity. Together, the principles of geometric and solid modeling form the foundation of 3D-computer-aided design and in general support the creation, exchange, visualization, animation, interrogation, and annotation of digital models of physical objects.
Angular velocityIn physics, angular velocity (symbol ω, sometimes Ω), also known as angular frequency vector, 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, , represents the angular speed (or angular frequency), the rate at which the object rotates (spins or revolves).
