Title: Theory / Unimportant / Experimental / Physics / Mechanics: Classical and Quantum - Taylor
Tags: LaTeXError hasSeenConjDef TypToProperty

Name: The force exerted on \(M\) by the spring
Definition: \(-Kx\)
Page: 1
Section: 01
Variables: \(x\) is the displacement from equilibrium,
\(M\) the mass
\(K\) the elastic constant
Notation: \(F_k\)
Property: Positive if it tends to increase \(x\)

Name: The equation of motion of the system
Definition: [$]M\ddot x+Kx=0[/$]
Page: 1, 2, 4
Chapter: 1
Section: 01
Variables: \(x\) is the displacement from equilibrium,
\(M\) the mass
\(K\) the elastic constant
Index: 002, 003, 011
Definition2: \(A\sin(\Omega t+\theta)\) with \(\Omega=\sqrt{\frac KM}\), \(A\) amplitude and \(\theta\) phase
Definition3: \(\sqrt{2E/K}\sin(\Omega (t+\theta))\) with \(\Omega=\sqrt{\frac KM}\), \(E\) the total energy and \(t_e\) a constant

Definition: [$]\dv{x}{t}[/$]
Page: 1
Section: 01
Variables: \(x\) a function of time \(t\)
Notation: \(\dot x\)

Definition: [$]\dv[2]{x}{t}[/$]
Page: 1
Section: 01
Variables: \(x\) a function of time \(t\)
Notation: [$]\ddot x[/$]

Name: The potential energy
Definition: \(\frac{Kx^2}2\)
Page: 2
Chapter: 1
Section: 01
Variables: \(x\) is the displacement from equilibrium,
\(M\) the mass
\(K\) the elastic constant
Notation: \(V(x)\)
Intuition: Energy stored in the spring when the displacement of \(M\) is increased from zero to \(x\)

Name: The total energy
Definition: The sum of the potential energy and of the kinetic energy
Page: 3
Chapter: 1
Section: 01
Variables: \(x\) is the displacement from equilibrium,
\(M\) the mass
\(K\) the elastic constant
Denoted by: \(E\)
Property: A constant of the motion

Name: Turning points of the motion
Definition: The points of intersection of the potential energy curve and of the total energy line
Page: 6
Chapter: 1
Section: 01

Name: A system in classical mechanics
Typ: A collection of particles
Page: 7
Section: 02
Chapter: 1

Name: A particle
Definition: An abstract object with a property called mass
Page: 7
Chapter: 1
Section: 02
Definition2: An object which can be acted upon by forces
Conjdef: Simultaneously
Definition3: An object which has at each point of time a position
Name2: A point-mass

Name: An internal force
Definition: A force from a particle of \(S\) upon another particle
Page: 7
Chapter: 1
Section: 02
Variables: \(S\) a system of classical mechanic

Name: An external force
Definition: A force arising from a source outside of \(S\)
Page: 7
Chapter: 1
Section: 02
Variables: \(S\) a system of classical mechanic

Name: The configuration of \(S\)
Definition: The totality of positions of the particules through time
Page: 8
Chapter: 1
Section: 02
Variables: \(S\) a system of classical mechanic
Typ: A point in a \(3N\)-dimensional space

Name: Unit vector
Page: 9
Chapter: 1
Section: 02
Notation: \(\mathbf e_x\), \(\mathbf e_y\) and \(\mathbf e_z\)

Definition: \(\mathbf e_xx_a+\mathbf e_yy_a+\mathbf e_zz_a\)
Page: 9
Chapter: 1
Section: 02
Variables: \(p\) a particle,
Notation: \(\mathbf r_a\)

Definition: The coordinates, in \(x\), \(y\) or \(z\), of a particle
Page: 9
Chapter: 1
Section: 02
Variables: \(p\) a particle,
Notation: The \(x_j\)