Force from acceleration and velocity

In special relativity, the Newton’s second law does not hold in the classical form \(\vec F = m \vec a\), but force can still be expressed via acceleration and velocity.

Conditions:

1. This law applies to special relativity.

Links:

1. Wikipedia, see paragraph.

force

Vector of the force exerted on the body.

Symbol:

F

Latex:

\({\vec F}\)

Dimension:

force

rest_mass

rest_mass of the body.

Symbol:

m_0

Latex:

\(m_{0}\)

Dimension:

mass

tangential_acceleration

Vector of the body’s acceleration tangential to the velocity vector.

Symbol:

a_t

Latex:

\({\vec a}_\text{t}\)

Dimension:

acceleration

normal_acceleration

Vector of the body’s acceleration normal to the velocity vector.

Symbol:

a_n

Latex:

\({\vec a}_\text{n}\)

Dimension:

acceleration

velocity

Vector of the body’s velocity. See speed.

Symbol:

v

Latex:

\({\vec v}\)

Dimension:

velocity

lorentz_factor

lorentz_factor.

Symbol:

gamma

Latex:

\(\gamma\)

Dimension:

dimensionless

law

F = gamma^3 * m_0 * a_t + gamma * m_0 * a_n

Latex:

\[{\vec F} = \gamma^{3} m_{0} {\vec a}_\text{t} + \gamma m_{0} {\vec a}_\text{n}\]