Eccentric Impact

 

Eccentric impact occurs when the line of impact of the collision is offset from one or both of the colliding body's mass centers.

 

 

If there are no external forces or moments applied to the bodies during the impact, or if they are small compared to the impact forces and moments, we can assume that linear momentum and angular momentum are conserved.

 

Linear momentum: m_Av_GA + m_Bv_GB = m_Av'_GA + m_Bv'_GB

 

Angular momentum: ∫∑M_G = I_G,2ω₂ - I_G,1ω₁

 

Plane of contact

 

Linear momentum is conserved for each body along the plane of contact.

 

(v_GA)_{plane of contact} = (v'_GA)_{plane of contact}

 

(v_GB)_{plane of contact} = (v'_GB)_{plane of contact}

 

Line of impact

 

Linear momentum is conserved for the system along the line of impact.

 

m_A(v_GA)_{line of impact} + m_B(v_GB)_{line of impact} = m_A(v'_GA)_{line of impact} + m_B(v'_GB)_{line of impact}

 

Coefficient of restitution

 

The coefficient of restitution is defined as the ratio between the relative velocity of separation and the relative velocity of approach.

 

e = ((v'_B)_{line of impact} - (v'_A)_{line of impact})/((v_A)_{line of impact} - (v_B)_{line of impact})