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7.-The quadrilateral acceleration is defined by: $a^\mu = \frac{du^\mu}{dt} = \frac{d^2x^\mu}{dt^2}$.Show that your components are related to the ordinary acceleration a and the velocity v by: $a^0 = \gamma^4 \mathbf{v} \cdot \mathbf{a}/c$ $a^1 = \gamma^2 \left[a_x + \gamma^2 \frac{v_x}{c^2} \mathbf{v} \cdot \mathbf{a}\right]$ $a^2 = \gamma^2 \left[a_y + \gamma^2 \frac{v_y}{c^2} \mathbf{v} \cdot \mathbf{a}\right]$ $a^3 = \gamma^2 \left[a_z + \gamma^2 \frac{v_z}{c^2} \mathbf{v} \cdot \mathbf{a}\right]$ where $\gamma = (1 - (v/c)^2)^{-1/2}$.

          7.-The quadrilateral acceleration is defined by: $a^\mu = \frac{du^\mu}{dt} = \frac{d^2x^\mu}{dt^2}$.Show that your components are related to the ordinary acceleration a and the velocity v by:
$a^0 = \gamma^4 \mathbf{v} \cdot \mathbf{a}/c$
$a^1 = \gamma^2 \left[a_x + \gamma^2 \frac{v_x}{c^2} \mathbf{v} \cdot \mathbf{a}\right]$
$a^2 = \gamma^2 \left[a_y + \gamma^2 \frac{v_y}{c^2} \mathbf{v} \cdot \mathbf{a}\right]$
$a^3 = \gamma^2 \left[a_z + \gamma^2 \frac{v_z}{c^2} \mathbf{v} \cdot \mathbf{a}\right]$
where $\gamma = (1 - (v/c)^2)^{-1/2}$.

7.-The quadrilateral acceleration is defined by: a^μ = (du^μ)/(dt) = (d^2x^μ)/(dt^2).Show that your components are related to the ordinary acceleration a and the velocity v by:
a^0 = γ^4 𝐯·𝐚/c
a^1 = γ^2 [ax + γ^2 (vx)/(c^2)𝐯·𝐚]
a^2 = γ^2 [ay + γ^2 (vy)/(c^2)𝐯·𝐚]
a^3 = γ^2 [az + γ^2 (vz)/(c^2)𝐯·𝐚]
where γ = (1 - (v/c)^2)^-1/2.

Added by Christopher P.

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