trochoid Synonyms
No Synonyms and anytonyms found
trochoid Meaning
trochoid (n.)
The curve described by any point in a wheel rolling on a line; a cycloid; a roulette; in general, the curve described by any point fixedly connected with a moving curve while the moving curve rolls without slipping on a second fixed curve, the curves all being in one plane. Cycloids, epicycloids, hypocycloids, cardioids, etc., are all trochoids.
trochoid (a.)
Admitting of rotation on an axis; -- sometimes applied to a pivot joint like that between the atlas and axis in the vertebral column.
Top-shaped; having a flat base and conical spire; -- said of certain shells.
Of or pertaining to the genus Trochus or family Trochidae.
trochoid Sentence Examples
- The trochoid curve generated by a point on a circle rolling without slipping along a straight line is a cycloid.
- The motion of a particle in a uniform magnetic field is a trochoid.
- The path of a projectile subject to constant gravity is a parabola, which is a special case of a trochoid.
- The surface traced by a point on the rim of a wheel rolling on a plane is a trochoid.
- The trochoid curve is a transcendental function that cannot be expressed in terms of elementary functions.
- The equation of a trochoid is given by the parametric equations x = a(θ - sin θ) and y = a(1 - cos θ), where a is the radius of the generating circle.
- The cycloid, which is a special case of a trochoid, is the curve of fastest descent between two points in a vertical plane.
- The brachistochrone problem, which seeks the path of quickest descent between two points in a vertical plane, can be solved using the concept of a trochoid.
- The trochoid curve is named after the Greek word "trochos," meaning wheel.
- The trochoid curve has applications in areas such as physics, engineering, and computer graphics.
FAQs About the word trochoid
The curve described by any point in a wheel rolling on a line; a cycloid; a roulette; in general, the curve described by any point fixedly connected with a movi
No synonyms found.
No antonyms found.
The trochoid curve generated by a point on a circle rolling without slipping along a straight line is a cycloid.
The motion of a particle in a uniform magnetic field is a trochoid.
The path of a projectile subject to constant gravity is a parabola, which is a special case of a trochoid.
The surface traced by a point on the rim of a wheel rolling on a plane is a trochoid.
