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Date of download: 10/8/2017 Copyright © ASME. All rights reserved.

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1 Date of download: 10/8/2017 Copyright © ASME. All rights reserved. From: Energetically Consistent Calculations for Oblique Impact in Unbalanced Systems With Friction J. Appl. Mech. 2015;82(8): doi: / Figure Legend: Impact configurations with positive unbalance β2 > 0 or negative unbalance β2 < 0

2 Date of download: 10/8/2017 Copyright © ASME. All rights reserved. From: Energetically Consistent Calculations for Oblique Impact in Unbalanced Systems With Friction J. Appl. Mech. 2015;82(8): doi: / Figure Legend: Normal and tangential components of relative velocity at C as functions of normal impulse during collision. The shaded areas represent work done by the normal impulse during compression and restitution.

3 Date of download: 10/8/2017 Copyright © ASME. All rights reserved. From: Energetically Consistent Calculations for Oblique Impact in Unbalanced Systems With Friction J. Appl. Mech. 2015;82(8): doi: / Figure Legend: Relative velocity components as function of normal impulse at C for all slip processes: (a) slip-stick for μ≥|μ¯|; (b) slip-reverse slip for β2 > 0 and μ<|μ¯|; (c) gross-slip for β2 < 0 and μ<|μ¯|; and (d) jam-stick for β2 < 0 and a large coefficient of friction μ≥-β3/β2

4 Date of download: 10/8/2017 Copyright © ASME. All rights reserved. From: Energetically Consistent Calculations for Oblique Impact in Unbalanced Systems With Friction J. Appl. Mech. 2015;82(8): doi: / Figure Legend: Slip processes for impact of a slender rod against a half-space as functions of the angle of inclination θ and the coefficient of friction μ

5 Date of download: 10/8/2017 Copyright © ASME. All rights reserved. From: Energetically Consistent Calculations for Oblique Impact in Unbalanced Systems With Friction J. Appl. Mech. 2015;82(8): doi: / Figure Legend: Kinematic (solid line) and kinetic (dashed line) CORs for elastic impact, e*=1, for normalized angle of incidence Ψ∧0 if unbalance is either positive, β2 > 0, or negative, β2 < 0

6 Date of download: 10/8/2017 Copyright © ASME. All rights reserved. From: Energetically Consistent Calculations for Oblique Impact in Unbalanced Systems With Friction J. Appl. Mech. 2015;82(8): doi: / Figure Legend: Slender bar with angle of inclination θ when it impacts at angle of incidence ψ0≡tan -1(-v1(0)/v3(0))=π/4 against a rough half-space. Configurations are shown with both (a) positive unbalance β2 > 0 and (b) negative unbalance β2 < 0.

7 Date of download: 10/8/2017 Copyright © ASME. All rights reserved. From: Energetically Consistent Calculations for Oblique Impact in Unbalanced Systems With Friction J. Appl. Mech. 2015;82(8): doi: / Figure Legend: (a) Kinematic and (b) kinetic COR for elastic impact (e*=1) of rigid rod inclined at angle θ that impacts at angle of incidence ψ0=π/4, against a rough half-space

8 Date of download: 10/8/2017 Copyright © ASME. All rights reserved. From: Energetically Consistent Calculations for Oblique Impact in Unbalanced Systems With Friction J. Appl. Mech. 2015;82(8): doi: / Figure Legend: Ratio of final to initial kinetic energy Tf/T0 as function of coefficient of friction μ for CORs eN = eP = e* = 1 used in analysis of oblique impact by rigid rod against rough elastic half-space. Rod inclination is (a) θ = π/6 rad (β2 > 0), or (b) θ = -π/6 rad (β2 < 0) and the angle of incidence is ψ0 = π/4.

9 Date of download: 10/8/2017 Copyright © ASME. All rights reserved. From: Energetically Consistent Calculations for Oblique Impact in Unbalanced Systems With Friction J. Appl. Mech. 2015;82(8): doi: / Figure Legend: Double pendulum that impacts against rough half space. Configurations are shown with either (a) positive unbalance, β2 > 0 or (b) negative unbalance, β2 < 0. In both cases the incident relative velocity at C is v(0) = 0.5343 n  n3.

10 Date of download: 10/8/2017 Copyright © ASME. All rights reserved. From: Energetically Consistent Calculations for Oblique Impact in Unbalanced Systems With Friction J. Appl. Mech. 2015;82(8): doi: / Figure Legend: (a) Kinematic and (b) kinetic COR for elastic impact (e*=1) of double pendulum that impacts at angle of incidence ψ0=1.105 rad, against a rough half-space


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