Classical mechanics (Symbols)¶
Symbols related to classical mechanics.
- force¶
Force is a vector quantity denoting an influence that can cause an object to change its velocity unless counterbalanced by other forces.
- Symbol:
F- Latex:
\(F\)
- Dimension:
force
- tension¶
Tension is the pulling or stretching force transmitted axially along an object so as to stretch it or pull it apart.
- Symbol:
T- Latex:
\(T\)
- Dimension:
force
- speed¶
Speed is the rate of change of the object’s position with respect to time. It is the scalar counterpart of the velocity vector, which is the rate of change of the object’s displacement with respect to time.
- Symbol:
v- Latex:
\(v\)
- Dimension:
velocity
- acceleration¶
Acceleration is the rate of change of the object’s velocity with respect to time. It is a vector quantity.
- Symbol:
a- Latex:
\(a\)
- Dimension:
acceleration
- position¶
Position is defined as the spatial location of an object with respect to a coordinate system.
- Symbol:
x- Latex:
\(x\)
- Dimension:
length
- euclidean_distance¶
Euclidean distance between two points is the length of the line segment between them. Mathematically, it can be represented by the following formula:
\[d = \sqrt{\left\Vert \mathbf{r}_2 - \mathbf{r}_1 \right\Vert},\]where \(\mathbf{r}_1\) is the position vector of the first point, \(\mathbf{r}_2\) is the position vector of the second point, and \(\left\Vert \cdot \right\Vert\) is the Euclidean norm.
Notes:
This symbol can be used for representing displacement. In that case, \(\mathbf{r}_1\) corresponds to the initial position of the body and \(\mathbf{r}_2\) to the final position of the body.
- Symbol:
d- Latex:
\(d\)
- Dimension:
length
- distance¶
distance, or more precisely total distance traveled, is the length of the path traced by a moving body. Mathematically, it can be represented by the following formula:
\[s(t) = \int \limits_0^t |\mathbf{v}(\tau)| d\tau,\]where \(\mathbf{v}\) is the velocity vector of the body as a function of time \(t\). It is assumed that the total distance traveled is zero at zero time.
Notes:
It is sometimes used in the sense of the length of space between two points, in which case
euclidean_distancemust be used.
- Symbol:
s- Latex:
\(s\)
- Dimension:
length
- distance_to_origin¶
Distance to the origin of the coordinate system.
- Symbol:
r- Latex:
\(r\)
- Dimension:
length
- distance_to_axis¶
Distance to reference axis.
- Symbol:
r- Latex:
\(r\)
- Dimension:
length
- length¶
Length is a measure of a size of an object.
- Symbol:
l- Latex:
\(l\)
- Dimension:
length
- radius¶
Radius of a sphere is the distance from the center of the sphere to any point on the sphere.
- Symbol:
r- Latex:
\(r\)
- Dimension:
length
- diameter¶
Diameter of a circle or sphere is the length of the biggest chord connecting two points on the circumference.
- Symbol:
D- Latex:
\(D\)
- Dimension:
length
- semimajor_axis¶
Semi-major axis, or major semiaxis, is the longest semidiameter of an ellipse.
- Symbol:
a- Latex:
\(a\)
- Dimension:
length
- semiminor_axis¶
Semi-minor axis, or minor semiaxis, is the smallest semidiameter of an ellipse.
- Symbol:
b- Latex:
\(b\)
- Dimension:
length
- thickness¶
Thickness is a measure of a size of an object, usually the separation between two layers, or the distance through an object distinct from length and width.
- Symbol:
h- Latex:
\(h\)
- Dimension:
length
- area¶
Area is the size of a region on a two-dimensional surface.
- Symbol:
A- Latex:
\(A\)
- Dimension:
area
- arc_length¶
Arc length is the distance between two points along a section of a curve.
- Symbol:
s- Latex:
\(s\)
- Dimension:
length
- angular_speed¶
Angular speed is the rate of change of angular distance with respect to time.
- Symbol:
w- Latex:
\(\omega\)
- Dimension:
angle/time
- angular_frequency¶
Angular frequency, also called angular rate, is a scalar measure of the temporal rate of change of the phase argument of a sinusoidal waveform or sine function.
- Symbol:
w- Latex:
\(\omega\)
- Dimension:
angle/time
- angular_acceleration¶
Angular acceleration is the rate of change of angular speed with respect to time.
- Symbol:
alpha- Latex:
\(\alpha\)
- Dimension:
angle/time**2
- angular_distance¶
Angular distance is a measure of an angular separation between two points.
- Symbol:
theta- Latex:
\(\theta\)
- Dimension:
angle
- angular_wavenumber¶
Angular wavenumber is the spatial analog of temporal frequency equal to radians per unit length.
- Symbol:
k- Latex:
\(k\)
- Dimension:
angle/length
- wavelength¶
Wavelength or spatial period is the distance over which the wave’s shape repeats.
- Symbol:
lambda- Latex:
\(\lambda\)
- Dimension:
length
- damping_ratio¶
Damping ratio is a dimensionless measure describing how oscillations in a system decay after a disturbance.
- Symbol:
zeta- Latex:
\(\zeta\)
- Dimension:
dimensionless
- volume¶
Volume is a measure of regions in three-dimensional space.
- Symbol:
V- Latex:
\(V\)
- Dimension:
volume
- impulse¶
Impulse is the change in momentum of an object.
- Symbol:
J- Latex:
\(J\)
- Dimension:
momentum
- phase_speed¶
Phase speed is the speed at which the phase of the wave travels.
- Symbol:
v- Latex:
\(v\)
- Dimension:
velocity
- group_speed¶
Group speed of a wave is the speed with which the overall envelope shape of the wave’s amplitudes, or the modulation or envelope of the wave, propagates through space.
- Symbol:
v_g- Latex:
\(v_\text{g}\)
- Dimension:
velocity
- pressure¶
Pressure is the force applied perpendicular to the surface of an object per unit area over which that force is distributed.
- Symbol:
p- Latex:
\(p\)
- Dimension:
pressure
- temporal_frequency¶
Temporal frequency is the number of occurrences of a repeating event per unit of time.
- Symbol:
f- Latex:
\(f\)
- Dimension:
frequency
- sound_intensity_level¶
Sound intensity level is the measure of the intensity of a sound relative to a reference value.
- Symbol:
L_I- Latex:
\(L_{I}\)
- Dimension:
dimensionless
- rotational_inertia¶
Rotational inertia, also known as moment of inertia, is defined relative to a rotational axis and is the ratio between the torque applied and the resulting angular acceleration about that axis.
- Symbol:
I- Latex:
\(I\)
- Dimension:
length**2*mass
- quality_factor¶
Quality factor or Q factor is a dimensionless parameter that describes how underdamped an oscillator or resonator is.
- Symbol:
Q- Latex:
\(Q\)
- Dimension:
dimensionless
- momentum¶
Momentum, more specifically linear or transitional momentum, is the product of the mass and velocity of an object.
- Symbol:
p- Latex:
\(p\)
- Dimension:
momentum
- mechanical_energy¶
Mechanical energy is defined to be the sum of potential energy and kinetic energy.
- Symbol:
E- Latex:
\(E\)
- Dimension:
energy
- kinetic_energy¶
Kinetic energy of an object is the form of energy that it possesses due to its motion.
- Symbol:
K- Latex:
\(K\)
- Dimension:
energy
- potential_energy¶
Potential energy is the energy held by an object because of its position relative to other objects, stresses within itself, its electric charge, or other factors. Potential energy is associated with so called conservative forces and only depends on the initial and final positions of the body in space.
- Symbol:
U- Latex:
\(U\)
- Dimension:
energy
- mass_flow_rate¶
Mass flow rate is the mass of a substance which passes per unit of time.
- Symbol:
mu- Latex:
\(\mu\)
- Dimension:
mass/time
- stiffness¶
Stiffness is the extent to which an object resists deformation in response to an applied force.
- Symbol:
k- Latex:
\(k\)
- Dimension:
force/length
- young_modulus¶
Young modulus is a mechanical property of solid materials that measures the tensile or compressive stiffness when the force is applied lengthwise.
- Symbol:
E- Latex:
\(E\)
- Dimension:
pressure
- phase_shift¶
Phase shift, also known as phase offset or phase difference, is the shift of phase between two periodic functions.
- Symbol:
phi- Latex:
\(\varphi\)
- Dimension:
angle
- phase¶
Phase of a wave or other periodic function of some real variable \(t\), such as time, is an angle-like quantity representing the fraction of the cycle covered up to \(t\).
- Symbol:
phi- Latex:
\(\varphi\)
- Dimension:
angle
- friction_coefficient¶
Coefficient of friction is a dimensionless scalar value which equals to the ratio of the force of friction between two bodies and the force pressing them together, either during or at the onset of slipping.
- Symbol:
mu- Latex:
\(\mu\)
- Dimension:
dimensionless
- height¶
Height is measure of vertical distance, either vertical extent or vertical position.
In the case of three-dimensional space, height is measured along the vertical z axis, describing a distance from (or “above”) the x-y plane.
- Symbol:
h- Latex:
\(h\)
- Dimension:
length
- torque¶
Torque is the turning effect of a force applied to a rotational system at a distance from the axis of rotation.
- Symbol:
tau- Latex:
\(\tau\)
- Dimension:
force*length
- torsion_stiffness¶
Torsion stiffness or torsion elastic modulus is equal to the change in torque required to twist the spring through an angle of 1 radian.
Links:
- Symbol:
kappa- Latex:
\(\kappa\)
- Dimension:
force*length/angle
- bulk_modulus¶
Bulk modulus of a substance is a measure of the resistance of a substance to bulk compression.
- Symbol:
K- Latex:
\(K\)
- Dimension:
pressure
- poisson_ratio¶
Poisson’s ratio is a measure of the Poisson effect, the deformation (expansion or contraction) of a material in directions perpendicular to the specific direction of loading.
- Symbol:
nu- Latex:
\(\nu\)
- Dimension:
dimensionless
- engineering_normal_strain¶
Engineering strain, also known as Cauchy strain, is expressed as the ratio of total deformation to the initial dimension of the material body on which forces are applied.
- Symbol:
e- Latex:
\(e\)
- Dimension:
dimensionless
- deformation¶
Deformation is a change in an object’s shape or form due to the application of a force or forces.
- Symbol:
Delta(l)- Latex:
\(\Delta l\)
- Dimension:
length
- strain¶
Strain is defined as relative deformation, compared to a reference position configuration.
- Symbol:
e- Latex:
\(e\)
- Dimension:
dimensionless
- stress¶
Stress is a physical quantity that describes forces present during deformation.
- Symbol:
sigma- Latex:
\(\sigma\)
- Dimension:
pressure
- mach_number¶
The Mach number is a dimensionless quantity in fluid dynamics representing the ratio of flow velocity past a boundary to the local speed of sound.
- Symbol:
M- Latex:
\(\text{M}\)
- Dimension:
dimensionless
- diffusion_coefficient¶
Diffusion coefficient, or diffusivity, is usually defined as the proportionality constant between the molar flux due to molecular diffusion and the negative value of the gradient in the concentration of the species.
Links:
- Symbol:
D- Latex:
\(D\)
- Dimension:
area/time
- dynamic_viscosity¶
Dynamic viscosity is a physical quantity measuring the resistance to deformation at a given rate. Specifically in fluid mechanics, it is the proportionality factor between the shear stress of the adjacent layers of the fluid and the local sheer velocity.
Links:
- Symbol:
mu- Latex:
\(\mu\)
- Dimension:
pressure*time
- diffusion_flux¶
Diffusion flux is a physical quantity that measures the amount of substance that will flow through a unit area during a unit time interval. For the general definition of flux, see Flux.
- Symbol:
J- Latex:
\(J\)
- Dimension:
amount_of_substance/(area*time)
- degrees_of_freedom¶
A degree of freedom is a physical parameter in the parameterization of a physical system. The number of degrees of freedom indicates the smallest number of parameters whose values determine all parameters in the chosen parameterization.
- Symbol:
f- Latex:
\(f\)
- Dimension:
dimensionless
- angular_momentum¶
Angular momentum, sometimes called rotational momentum, is the rotational analog of linear
momentum.- Symbol:
L- Latex:
\(L\)
- Dimension:
length**2*mass/time
- latitude¶
Latitude is a coordinate that specifies the north-south position of a point on the surface of the Earth or another celestial body. Its value ranges from \(-90^\circ\) at the south pole to \(90^\circ\) at the north pole, with \(0^\circ\) at the Equator.
- Symbol:
phi- Latex:
\(\phi\)
- Dimension:
angle
- longitude¶
Longitude is a coordinate that specifies the east-west position of a point on the surface of the Earth, or another celestial body. The prime meridian defines \(0^\circ\) longitude; positive longitudes are east of the prime meridian, and the negative ones are west.
- Symbol:
lambda- Latex:
\(\lambda\)
- Dimension:
angle
- sector_speed¶
Areal speed, also called sector speed or sectorial speed, is a quantity that indicates the rate of change at which
areais swept out by a particle as it moves along a curve. The calculation of the area swept can be found in the link below.Links:
- Symbol:
sigma- Latex:
\(\sigma\)
- Dimension:
area/time
- kepler_constant¶
The Kepler’s constant is the constant of proportionality in Kepler’s third law of planetary motion, namely the ratio between the square of the period of the planet to the semi-major axis of the planet’s orbit. It is constant for all objects orbiting around the same object.
- Symbol:
K- Latex:
\(\mathfrak{K}\)
- Dimension:
length**3/time**2
- surface_tension¶
Surface tension, as a phenomenon, is the tendency of liquid surfaces at rest to shrink into the minimum surface area possible. The coefficient of surface tension is directly proportional to the force necessary to increase the surface area of the fluid and inversely proportional to the length of the side at which the force is applied to.
Links:
- Symbol:
gamma- Latex:
\(\gamma\)
- Dimension:
force/length