Acceleration from force and velocity¶

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

Notation:

\(c\) (c) is speed_of_light.

Conditions:

This law applies to special relativity.

Links:

Wikipedia, see paragraph.

acceleration¶: Vector of the body’s acceleration.

Symbol:: a
Latex:: \({\vec a}\)
Dimension:: acceleration

rest_mass¶: rest_mass of the body.

Symbol:: m_0
Latex:: \(m_{0}\)
Dimension:: mass

force¶: Vector of the force exerted on the body.

Symbol:: F
Latex:: \({\vec F}\)
Dimension:: force

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¶

a = (F - dot(F, v) / c^2 * v) / (m_0 * gamma)

Latex:: \[{\vec a} = \frac{{\vec F} - \frac{\left( {\vec F}, {\vec v} \right)}{c^{2}} {\vec v}}{m_{0} \gamma}\]