sem0501-aula25 - edisciplinas.usp.br
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São Carlos, 19/11/19
ARCLabLaboratório de Controle de Robótica Avancada
SEM0501Dinâmica Aplicada às Máquinas
Prof. Dr. Thiago Boaventura [email protected]
Aula #25 — Princípios do impulso e momento linear e angular para
corpos rígidosARCLab
Laboratório de Controle de Robótica Avancada
SEM0501 — Prof. Dr. Thiago BoaventuraARCLab
https://www.youtube.com/watch?v=jNElhXTf6Fs
Flying trapeze:ARCLabLaboratório de Controle de Robótica Avancada
SEM0501 — Prof. Dr. Thiago BoaventuraSEM0501 — Prof. Dr. Thiago Boaventura
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ARCLab
Princípio do impulso e momento linear e angular para partículas
mv1 +XZ t2
t1
F dt = mv2
H1 +XZ t2
t1
M dt = H2
ARCLabLaboratório de Controle de Robótica Avancada
SEM0501 — Prof. Dr. Thiago BoaventuraSEM0501 — Prof. Dr. Thiago Boaventura
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ARCLab
Momento angular
Momento linear:
Momento angular:
L = mv
ARCLabLaboratório de Controle de Robótica Avancada
SEM0501 — Prof. Dr. Thiago BoaventuraSEM0501 — Prof. Dr. Thiago Boaventura
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ARCLab
Momento angular
L = mv
H = r⇥mv<latexit sha1_base64="9/nn9uHXScWAEBjkApG9RXtqdaE=">AAACJ3icbZDLSsNAFIYn9VbrrerSzWARuiqJCLoRim66rGAv0IQymU7aoZNMmDkplNJX8D3cu9VXcCe6dOdjOGmj2NYDAx//uc7vx4JrsO0PK7e2vrG5ld8u7Ozu7R8UD4+aWiaKsgaVQqq2TzQTPGIN4CBYO1aMhL5gLX94m+ZbI6Y0l9E9jGPmhaQf8YBTAkbqFstuSGDgB7iGr/EPK+wCD5nG4a806hZLdsWeBV4FJ4MSyqLeLX65PUmTkEVABdG649gxeBOigFPBpgU30SwmdEj6rGMwImahN5n9aIrPjNLDgVTmRYBn6t+OCQm1Hoe+qUwP1Mu5VPwv10kguPImPIoTYBGdLwoSgUHi1B7c44pREGMDhCpubsV0QBShYExc2JLOBimFnhprnGUjVqF5XnEM312UqjeZSXl0gk5RGTnoElVRDdVRA1H0gJ7QM3qxHq1X6816n5fmrKznGC2E9fkNLf+lyQ==</latexit><latexit sha1_base64="9/nn9uHXScWAEBjkApG9RXtqdaE=">AAACJ3icbZDLSsNAFIYn9VbrrerSzWARuiqJCLoRim66rGAv0IQymU7aoZNMmDkplNJX8D3cu9VXcCe6dOdjOGmj2NYDAx//uc7vx4JrsO0PK7e2vrG5ld8u7Ozu7R8UD4+aWiaKsgaVQqq2TzQTPGIN4CBYO1aMhL5gLX94m+ZbI6Y0l9E9jGPmhaQf8YBTAkbqFstuSGDgB7iGr/EPK+wCD5nG4a806hZLdsWeBV4FJ4MSyqLeLX65PUmTkEVABdG649gxeBOigFPBpgU30SwmdEj6rGMwImahN5n9aIrPjNLDgVTmRYBn6t+OCQm1Hoe+qUwP1Mu5VPwv10kguPImPIoTYBGdLwoSgUHi1B7c44pREGMDhCpubsV0QBShYExc2JLOBimFnhprnGUjVqF5XnEM312UqjeZSXl0gk5RGTnoElVRDdVRA1H0gJ7QM3qxHq1X6816n5fmrKznGC2E9fkNLf+lyQ==</latexit><latexit sha1_base64="9/nn9uHXScWAEBjkApG9RXtqdaE=">AAACJ3icbZDLSsNAFIYn9VbrrerSzWARuiqJCLoRim66rGAv0IQymU7aoZNMmDkplNJX8D3cu9VXcCe6dOdjOGmj2NYDAx//uc7vx4JrsO0PK7e2vrG5ld8u7Ozu7R8UD4+aWiaKsgaVQqq2TzQTPGIN4CBYO1aMhL5gLX94m+ZbI6Y0l9E9jGPmhaQf8YBTAkbqFstuSGDgB7iGr/EPK+wCD5nG4a806hZLdsWeBV4FJ4MSyqLeLX65PUmTkEVABdG649gxeBOigFPBpgU30SwmdEj6rGMwImahN5n9aIrPjNLDgVTmRYBn6t+OCQm1Hoe+qUwP1Mu5VPwv10kguPImPIoTYBGdLwoSgUHi1B7c44pREGMDhCpubsV0QBShYExc2JLOBimFnhprnGUjVqF5XnEM312UqjeZSXl0gk5RGTnoElVRDdVRA1H0gJ7QM3qxHq1X6816n5fmrKznGC2E9fkNLf+lyQ==</latexit><latexit sha1_base64="9/nn9uHXScWAEBjkApG9RXtqdaE=">AAACJ3icbZDLSsNAFIYn9VbrrerSzWARuiqJCLoRim66rGAv0IQymU7aoZNMmDkplNJX8D3cu9VXcCe6dOdjOGmj2NYDAx//uc7vx4JrsO0PK7e2vrG5ld8u7Ozu7R8UD4+aWiaKsgaVQqq2TzQTPGIN4CBYO1aMhL5gLX94m+ZbI6Y0l9E9jGPmhaQf8YBTAkbqFstuSGDgB7iGr/EPK+wCD5nG4a806hZLdsWeBV4FJ4MSyqLeLX65PUmTkEVABdG649gxeBOigFPBpgU30SwmdEj6rGMwImahN5n9aIrPjNLDgVTmRYBn6t+OCQm1Hoe+qUwP1Mu5VPwv10kguPImPIoTYBGdLwoSgUHi1B7c44pREGMDhCpubsV0QBShYExc2JLOBimFnhprnGUjVqF5XnEM312UqjeZSXl0gk5RGTnoElVRDdVRA1H0gJ7QM3qxHq1X6816n5fmrKznGC2E9fkNLf+lyQ==</latexit>
H = rmvsen(✓)<latexit sha1_base64="3xxSdzjDAYuLbg5Jkk4fIWydpGU=">AAACFHicbZDPSgMxEMaz/v9vVTx5CRahXsquCHoRRC89VrAqtEvJprNtaDZZktlCWfoa3r3qK3gTr959Ax/DbO3BWj8I/PhmJjN8USqFRd//9ObmFxaXlldW19Y3Nre2Szu7d1ZnhkODa6nNQ8QsSKGggQIlPKQGWBJJuI/610X9fgDGCq1ucZhCmLCuErHgDJ3VLu3X6AU1NKEDakFVWtgDZMftUtmv+mPRWQgmUCYT1dulr1ZH8ywBhVwya5uBn2KYM4OCSxittTILKeN91oWmQ8USsGE+Pn9Ej5zTobE27imkY/f3RM4Sa4dJ5DoThj37t1aY/9WaGcbnYS5UmiEo/rMoziRFTYssaEcY4CiHDhg3wt1KeY8ZxtElNrWl+Bu1lnbkogn+BjELdyfVwPHNafnyahLSCjkgh6RCAnJGLkmN1EmDcJKTJ/JMXrxH79V7895/Wue8ycwemZL38Q3+553M</latexit><latexit sha1_base64="3xxSdzjDAYuLbg5Jkk4fIWydpGU=">AAACFHicbZDPSgMxEMaz/v9vVTx5CRahXsquCHoRRC89VrAqtEvJprNtaDZZktlCWfoa3r3qK3gTr959Ax/DbO3BWj8I/PhmJjN8USqFRd//9ObmFxaXlldW19Y3Nre2Szu7d1ZnhkODa6nNQ8QsSKGggQIlPKQGWBJJuI/610X9fgDGCq1ucZhCmLCuErHgDJ3VLu3X6AU1NKEDakFVWtgDZMftUtmv+mPRWQgmUCYT1dulr1ZH8ywBhVwya5uBn2KYM4OCSxittTILKeN91oWmQ8USsGE+Pn9Ej5zTobE27imkY/f3RM4Sa4dJ5DoThj37t1aY/9WaGcbnYS5UmiEo/rMoziRFTYssaEcY4CiHDhg3wt1KeY8ZxtElNrWl+Bu1lnbkogn+BjELdyfVwPHNafnyahLSCjkgh6RCAnJGLkmN1EmDcJKTJ/JMXrxH79V7895/Wue8ycwemZL38Q3+553M</latexit><latexit sha1_base64="3xxSdzjDAYuLbg5Jkk4fIWydpGU=">AAACFHicbZDPSgMxEMaz/v9vVTx5CRahXsquCHoRRC89VrAqtEvJprNtaDZZktlCWfoa3r3qK3gTr959Ax/DbO3BWj8I/PhmJjN8USqFRd//9ObmFxaXlldW19Y3Nre2Szu7d1ZnhkODa6nNQ8QsSKGggQIlPKQGWBJJuI/610X9fgDGCq1ucZhCmLCuErHgDJ3VLu3X6AU1NKEDakFVWtgDZMftUtmv+mPRWQgmUCYT1dulr1ZH8ywBhVwya5uBn2KYM4OCSxittTILKeN91oWmQ8USsGE+Pn9Ej5zTobE27imkY/f3RM4Sa4dJ5DoThj37t1aY/9WaGcbnYS5UmiEo/rMoziRFTYssaEcY4CiHDhg3wt1KeY8ZxtElNrWl+Bu1lnbkogn+BjELdyfVwPHNafnyahLSCjkgh6RCAnJGLkmN1EmDcJKTJ/JMXrxH79V7895/Wue8ycwemZL38Q3+553M</latexit><latexit sha1_base64="3xxSdzjDAYuLbg5Jkk4fIWydpGU=">AAACFHicbZDPSgMxEMaz/v9vVTx5CRahXsquCHoRRC89VrAqtEvJprNtaDZZktlCWfoa3r3qK3gTr959Ax/DbO3BWj8I/PhmJjN8USqFRd//9ObmFxaXlldW19Y3Nre2Szu7d1ZnhkODa6nNQ8QsSKGggQIlPKQGWBJJuI/610X9fgDGCq1ucZhCmLCuErHgDJ3VLu3X6AU1NKEDakFVWtgDZMftUtmv+mPRWQgmUCYT1dulr1ZH8ywBhVwya5uBn2KYM4OCSxittTILKeN91oWmQ8USsGE+Pn9Ej5zTobE27imkY/f3RM4Sa4dJ5DoThj37t1aY/9WaGcbnYS5UmiEo/rMoziRFTYssaEcY4CiHDhg3wt1KeY8ZxtElNrWl+Bu1lnbkogn+BjELdyfVwPHNafnyahLSCjkgh6RCAnJGLkmN1EmDcJKTJ/JMXrxH79V7895/Wue8ycwemZL38Q3+553M</latexit>
Para velocidade tangencial:
<latexit sha1_base64="zMRVbvlp2Y3oY6aJNlhjtjZhPfQ=">AAACDnicbZDLSgMxFIYz9VbrpaMu3QSL4KrMiKAboeimywr2Au1QMmnahmaSITlTKEPfwb1bfQV34tZX8A18DDPtLGz1h8DHf87JOfxhLLgBz/tyChubW9s7xd3S3v7BYdk9Om4ZlWjKmlQJpTshMUxwyZrAQbBOrBmJQsHa4eQ+q7enTBuu5CPMYhZEZCT5kFMC1uq75Tq+xRpHeNpPgch53614VW8h/Bf8HCooV6PvfvcGiiYRk0AFMabrezEEKdHAqWDzUi8xLCZ0Qkasa1GSiJkgXRw+x+fWGeCh0vZJwAv390RKImNmUWg7IwJjs17LzP9q3QSGN0HKZZwAk3S5aJgIDApnKeAB14yCmFkgVHN7K6ZjogkFm9XKluxvUEqYLBp/PYi/0Lqs+pYfriq1uzykIjpFZ+gC+ega1VAdNVATUZSgZ/SCXp0n5815dz6WrQUnnzlBK3I+fwCCGJwB</latexit>
ARCLabLaboratório de Controle de Robótica Avancada
SEM0501 — Prof. Dr. Thiago BoaventuraSEM0501 — Prof. Dr. Thiago Boaventura
Revis
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ARCLab
Momento linear para corpos rígidos
m
v vL L
L = mv
m
ARCLabLaboratório de Controle de Robótica Avancada
SEM0501 — Prof. Dr. Thiago BoaventuraSEM0501 — Prof. Dr. Thiago Boaventura
Revis
ão au
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ARCLab
Momento angular para corpos rígidos
Momento linear:
Momento angular:
vARCLab
Laboratório de Controle de Robótica Avancada
SEM0501 — Prof. Dr. Thiago BoaventuraARCLab
Momento angular para corpos rígidos
HG = IG!
HA = IA!
HA = IG! + (mvG)d
ARCLabLaboratório de Controle de Robótica Avancada
SEM0501 — Prof. Dr. Thiago BoaventuraARCLab
Princípio do impulso e momento linear e angular para corpos rígidos
mv1 +XZ t2
t1
F dt = mv2
H1 +XZ t2
t1
M dt = H2
mvG1 +XZ t2
t1
F dt = mvG2
IO!1 +XZ
t2
t1
MO dt = IO!2
ARCLabLaboratório de Controle de Robótica Avancada
SEM0501 — Prof. Dr. Thiago BoaventuraARCLab
Problema 19.2
ARCLabLaboratório de Controle de Robótica Avancada
SEM0501 — Prof. Dr. Thiago BoaventuraARCLab
Problema 19.4
ARCLabLaboratório de Controle de Robótica Avancada
SEM0501 — Prof. Dr. Thiago BoaventuraARCLab
https://www.youtube.com/watch?v=C7w2QwjJAmM
Impacto excêntrico de corpos rígidos:ARCLabLaboratório de Controle de Robótica Avancada
SEM0501 — Prof. Dr. Thiago BoaventuraARCLab
Impacto excêntrico em corpos rígidos
H1 = H2
e =vB2 � vA2
vA1 � vB1ARCLabLaboratório de Controle de Robótica Avancada
SEM0501 — Prof. Dr. Thiago BoaventuraARCLab
Problema 19.47
ARCLabLaboratório de Controle de Robótica Avancada
SEM0501 — Prof. Dr. Thiago BoaventuraARCLab
Lista de exercícios para próxima aula…
19.1, 19.10, 19.17, 19.27, 19.38
ARCLabLaboratório de Controle de Robótica Avancada
SEM0501 — Prof. Dr. Thiago BoaventuraARCLab
Dúvidas?
ARCLabLaboratório de Controle de Robótica Avancada
ARCLabLaboratório de Controle de Robótica Avancada