This website uses cookies to ensure you get the best experience. Learn more

statics

In 1860 he was appointed to the professorship of higher geometry at the university of Bologna, and in 1866 to that of higher geometry and graphical statics at the higher technical college of Milan.

10The literature of graphical statics and its technical applications is very extensive.

10His manual on Graphical Statics and his Elements of Projective Geometry (translated by C. Leudesdorf), have been published in English by the Clarendon Press.

00These headings are: "Geometry and Kinematics of Particles and Solid Bodies"; "Principles of Rational Mechanics"; "Statics of Particles, Rigid Bodies, &c."; "Kinetics of Particles, Rigid Bodies, &c."; "General Analytical Mechanics"; "Statics and Dynamics of Fluids"; "Hydraulics and Fluid Resistances"; "Elasticity."

00He also published two larger works, Social Statics in 1850, and Principles of Psychology in 1855.

001850, Social Statics.

00This function is also called the " thermodynamic potential at constant volume " from the analogy with the condition of minimum potential energy as the criterion of stable equilibrium in statics.

00C. Turner, Graphics applied to Arithmetic, Mensuration and Statics (1907).

00It should be noted that, within a limited range of application to terrestrial mechanics, the most convenient way of attacking the question of the relations of forces to the physical statics.

00in its account of the concept, it brings the statics of knowledge, so to speak, into integral relation with the dynamics.

00The subject is usually expounded under the two divisions of statics and kinetics, the former dealing with the conditions of rest or equilibrium and the latter with the phenomena of motion as affected by force.

00We follow als the traditional practice of dealing first with statics and thel with kinetics.

00Statics of a particle.

00Statics of a system of particles.

00Plane statics.

00Graphical statics.

00Three-dimensional statics.

00Statics of inextensible chains.

00Statics of a Particle.By a particle is meant a body whose position can for the purpose in hand be sufficiently specified by a mathematical point.

00In most questions of pure statics we are concerned only with the ratios of the various forces which enter into the problem, so that it is indifferent what unit of force is adopted.

00Statics of a System of ParticlesWe assume that the mutual forces between the pairs of particles, whatever their nature, are subject to the Law of Action and Reaction (Newtons Third Law); i.e.

00Plane Stalics.The statics of a rigid body rests on the following two assumptions:

00independent entity in statics.

00Statics of Inextensible Chains.The theory of bodies or structures which are deformable in their smallest parts belongs properly to elasticity.

00The case of inextensible strings or chains is, however, so simple that it is generally included in expositions of pure statics.

00Examples will be found in textbooks of the calculus and of analytical statics.

00The question remains, of course, as to how far the measurement of force here implied is practically consistent with the gravitational method usually adopted in statics; this will be referred to presently.

00Kinetics of a System of Discrete Particles.The momenta of the several particles constitute a system of localized vectors which, for purposes of resolving and taking moments, may be reduced like a system of forces in statics (~ 8).

00This is subject tc the same relations as a couple in statics; it may be represented by a vector which will, however, in general vary with the position of 0.

00Routh, Analytical Statics (2nd.

00Minchin, Statics (4th ed., oxford, 1888); A.

00This principle of least resistance renders determinate many problems in the statics of structures which were formerly considered indeterminate.

00Relations between Polygons of Loads and of Resistances.In a structure in which each piece is supported at two joints only, the well-known laws of statics show that the directions of the gross load on each piece and of the two resistances by which it is supported must lie in one plane, must either be parallel or meet in one point, and must bear to each other, if not parallel, the proportions of the sides of a triangle respectively parallel to their directions, and, if parallel, such proportions that each of the three forces shall be proportional to the distance between the other two,all the three distances being measured along one direction.

00According to a well-known principle of statics, because the loads or external pressures P1L~, &c., balance each other, they must be proportional to the sides of a closed polygon drawn respectively parallel to their directions.

00In the polygon of loads the direction of a load sustained by parallel resistances traverses the point O-i i Since the relation discussed in 7 was enunciated by Rankine, an enormous development has taken place in the subject of Graphic Statics, the first comprehensive textbook on the subject being Die Graphische Statik by K.

00Joint; then, by the principles of statics, - - the component of the resistance normal to the joint is CP=CR.cos PCR;

00The mode of distribution of a force applied to a solid body requires to be considered when its stiffness and strength are treated of; but, in questions respecting the action of a force upon a rigid body considered as a whole, the resultant of the distributed force, determined according to the principles of statics, and considered as acting in a single line and applied at a single point, may, for the occasion, be substituted for the force as really distributed.

00Forces applied to Mechanism Classed.If 0 be the obliquity of a force F applied to a piece of a machinethat is, the angle made by the direction of the force with the direction of motion of its point of applicationthen by the principles of statics, F may be resolved into two rectangular components, viz.

00Now from the laws of statics it is known that, in order that a system of forces applied to a system of connected points may be in equilibrium, it is necessary that the sum formed by putting together the products of the forces by the respective distances through which their points of application are capable of moving simultaneously, each along the direction of the force applied to it, shall be zero, products being considered positive or negative according as, the direction of the forces and the possible motions of their points of application are the same or opposite.

00Let the useful resistance and the weight of the piece be compounded by the principles of statics into one force, and let this be called the given force.

00Then, according to a well-known principle in statics, the normal pressure at the elementary arc do is TdO, T being the mean tension of the band at that elementary arc; consequently the friction on that arc is dF =JTdo.

00According to the principles of statics, the resultant of the force P, applied at G perpendicular to the plane OG, and the couple M is a force equal and parallel to P, but applied at a distance GC from G, in the prolongation of the perpendicular OG, whose value is GC = M/P = R2/OG.

00He made considerable contributions to scientific literature, and among his publications were: An Analytical View of Newton's Principia, with Lord Brougham (1855); an Essay on the Stability of a given State of Motion, which won the Adams' prize in 1877; and treatises on the Dynamics of Rigid Bodies, on Analytical Statics, and on the Dynamics of a Particle.

00Meanwhile he was filling his note-books as busily as ever with the results of his studies in statics and dynamics, in human anatomy, geometry and the phenomena of light and shade.

00It was his duty as professor to lecture at least once a week in term time on some portion of geometry, arithmetic, astronomy, geography, optics, statics, or some other mathematical subject, and also for two hours in the week to allow an audience to any student who might come to consult with the professor on any difficulties he had met with.

00We have thus a statics and a mechanics of mind which investigate respectively the conditions of equilibrium and of movement among presentations.

00In the statics two magnitudes have to be determined: (I) the amount of the suppression or inhibition (Hemmungssumme), and (2) the ratio in which this is shared among the opposing presentations.

00It reviews the principles of statics and kinematics and applying them to the approximate analysis of pin and rigid jointed frames.

00statics results hold for emissions trading?

00statics problems.

00In 1860 he was appointed to the professorship of higher geometry at the university of Bologna, and in 1866 to that of higher geometry and graphical statics at the higher technical college of Milan.

00His manual on Graphical Statics and his Elements of Projective Geometry (translated by C. Leudesdorf), have been published in English by the Clarendon Press.

00These headings are: "Geometry and Kinematics of Particles and Solid Bodies"; "Principles of Rational Mechanics"; "Statics of Particles, Rigid Bodies, &c."; "Kinetics of Particles, Rigid Bodies, &c."; "General Analytical Mechanics"; "Statics and Dynamics of Fluids"; "Hydraulics and Fluid Resistances"; "Elasticity."

00He also published two larger works, Social Statics in 1850, and Principles of Psychology in 1855.

00In Social Statics (1850) he still regards the process teleologically, and argues after the fashion of Paley that "the greatest happiness is the purpose of creation" (ch.

001850, Social Statics.

00This function is also called the " thermodynamic potential at constant volume " from the analogy with the condition of minimum potential energy as the criterion of stable equilibrium in statics.

00== Treatise on the Differential Calculus and the Elements of the Integral Calculus (1852, 6th ed., 1873), Treatise on Analytical Statics (1853, 4th ed., 1874); Treatise on the Integral Calculus (1857, 4th ed., 1874); Treatise on Algebra (1858, 6th ed., 1871); Treatise on Plane Coordinate Geometry (1858, 3rd ed., 1861); Plane Trigonometry (1859, 4th ed., 1869); Spherical Trigonometry (1859); History of the Calculus of Variations (1861); Theory of Equations (1861, 2nd ed.

00C. Turner, Graphics applied to Arithmetic, Mensuration and Statics (1907).

00The external forces on a frame or bridge in equilibrium under those forces may, by a well-known proposition in statics, be represented by a closed polygon, each side of which is parallel to one force, and represents the force in magnitude as well as in direction.

00It should be noted that, within a limited range of application to terrestrial mechanics, the most convenient way of attacking the question of the relations of forces to the physical statics.

00in its account of the concept, it brings the statics of knowledge, so to speak, into integral relation with the dynamics.

00presence of what is at least an important half-truth, which intellectuallism with its statics of the rational order viewed as a completely articulate system has tended to ignore.

00Glass is still commonly used as a dielectric because of its cheapness, high dielectric strength or resistance to electric puncture, and its high dielectric constant (see Electro Statics).

00The subject is usually expounded under the two divisions of statics and kinetics, the former dealing with the conditions of rest or equilibrium and the latter with the phenomena of motion as affected by force.

00We follow als the traditional practice of dealing first with statics and thel with kinetics.

00Statics of a particle.

00Statics of a system of particles.

00Plane statics.

00Graphical statics.

00Three-dimensional statics.

00Statics of inextensible chains.

00Statics of a Particle.By a particle is meant a body whose position can for the purpose in hand be sufficiently specified by a mathematical point.

00In most questions of pure statics we are concerned only with the ratios of the various forces which enter into the problem, so that it is indifferent what unit of force is adopted.

00Statics of a System of ParticlesWe assume that the mutual forces between the pairs of particles, whatever their nature, are subject to the Law of Action and Reaction (Newtons Third Law); i.e.

00Plane Stalics.The statics of a rigid body rests on the following two assumptions:

00independent entity in statics.

00Statics of Inextensible Chains.The theory of bodies or structures which are deformable in their smallest parts belongs properly to elasticity.

00The case of inextensible strings or chains is, however, so simple that it is generally included in expositions of pure statics.

00Examples will be found in textbooks of the calculus and of analytical statics.

00The question remains, of course, as to how far the measurement of force here implied is practically consistent with the gravitational method usually adopted in statics; this will be referred to presently.

00Kinetics of a System of Discrete Particles.The momenta of the several particles constitute a system of localized vectors which, for purposes of resolving and taking moments, may be reduced like a system of forces in statics (~ 8).

00This is subject tc the same relations as a couple in statics; it may be represented by a vector which will, however, in general vary with the position of 0.

00Routh, Analytical Statics (2nd.

00Minchin, Statics (4th ed., oxford, 1888); A.

00The literature of graphical statics and its technical applications is very extensive.

00This principle of least resistance renders determinate many problems in the statics of structures which were formerly considered indeterminate.

00Relations between Polygons of Loads and of Resistances.In a structure in which each piece is supported at two joints only, the well-known laws of statics show that the directions of the gross load on each piece and of the two resistances by which it is supported must lie in one plane, must either be parallel or meet in one point, and must bear to each other, if not parallel, the proportions of the sides of a triangle respectively parallel to their directions, and, if parallel, such proportions that each of the three forces shall be proportional to the distance between the other two,all the three distances being measured along one direction.

00According to a well-known principle of statics, because the loads or external pressures P1L~, &c., balance each other, they must be proportional to the sides of a closed polygon drawn respectively parallel to their directions.

00In the polygon of loads the direction of a load sustained by parallel resistances traverses the point O-i i Since the relation discussed in 7 was enunciated by Rankine, an enormous development has taken place in the subject of Graphic Statics, the first comprehensive textbook on the subject being Die Graphische Statik by K.

00Joint; then, by the principles of statics, - - the component of the resistance normal to the joint is CP=CR.cos PCR;

00The mode of distribution of a force applied to a solid body requires to be considered when its stiffness and strength are treated of; but, in questions respecting the action of a force upon a rigid body considered as a whole, the resultant of the distributed force, determined according to the principles of statics, and considered as acting in a single line and applied at a single point, may, for the occasion, be substituted for the force as really distributed.

00Forces applied to Mechanism Classed.If 0 be the obliquity of a force F applied to a piece of a machinethat is, the angle made by the direction of the force with the direction of motion of its point of applicationthen by the principles of statics, F may be resolved into two rectangular components, viz.

00Now from the laws of statics it is known that, in order that a system of forces applied to a system of connected points may be in equilibrium, it is necessary that the sum formed by putting together the products of the forces by the respective distances through which their points of application are capable of moving simultaneously, each along the direction of the force applied to it, shall be zero, products being considered positive or negative according as, the direction of the forces and the possible motions of their points of application are the same or opposite.

00Let the useful resistance and the weight of the piece be compounded by the principles of statics into one force, and let this be called the given force.

00Then, according to a well-known principle in statics, the normal pressure at the elementary arc do is TdO, T being the mean tension of the band at that elementary arc; consequently the friction on that arc is dF =JTdo.

00According to the principles of statics, the resultant of the force P, applied at G perpendicular to the plane OG, and the couple M is a force equal and parallel to P, but applied at a distance GC from G, in the prolongation of the perpendicular OG, whose value is GC = M/P = R2/OG.

00He made considerable contributions to scientific literature, and among his publications were: An Analytical View of Newton's Principia, with Lord Brougham (1855); an Essay on the Stability of a given State of Motion, which won the Adams' prize in 1877; and treatises on the Dynamics of Rigid Bodies, on Analytical Statics, and on the Dynamics of a Particle.

00Meanwhile he was filling his note-books as busily as ever with the results of his studies in statics and dynamics, in human anatomy, geometry and the phenomena of light and shade.

00STATICS (from Gr.

00It was his duty as professor to lecture at least once a week in term time on some portion of geometry, arithmetic, astronomy, geography, optics, statics, or some other mathematical subject, and also for two hours in the week to allow an audience to any student who might come to consult with the professor on any difficulties he had met with.

00We have thus a statics and a mechanics of mind which investigate respectively the conditions of equilibrium and of movement among presentations.

00In the statics two magnitudes have to be determined: (I) the amount of the suppression or inhibition (Hemmungssumme), and (2) the ratio in which this is shared among the opposing presentations.

00Do natural comparative statics results hold for emissions trading?

00Section 4 describes the application of concepts and principles to statics problems.

00Hopefully these statics will convince everyone that it simply isn't worth the risk to drink and drive, especially during the holidays when people are more likely to imbibe.

00In light of these disturbing safety statics, you may be wondering what can be done to keep your child safe while supporting National Playground Safety Week.

00STATICS (from Gr.

01

The word usage examples above have been gathered from various sources to reflect current and historial usage. They do not represent the opinions of YourDictionary.com.