Deret Tak Hingga, Uji Kekonvergenan Deret, Deret Taylor Dan Deret Maclaurin (9
Mekanika Lanjut Deret Taylor
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URAIAN TAYLOR DALAM KURUNG POISSON UNTUK 2 BANDUL
Saturday, 24 Mei 2014
Oleh: Kelompok 4Atikah Mayangsari (1211703006)Cut Wulandayu (1211703008)Gina Nurdiani D.A (1211703016)Lida Maulida (1211703021)Siti Mariam (1211703033)
PERSENTASI MEKANIKA LANJUT
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3. Gunakan uraian Taylor dalam kurung poisson untuk menurunkan persamaan gerak dari ayunan rangkap seperti gambar berikut, andaikan amplitude sangat kecil.
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SUMBU X
SUMBU Y
KOORDINAT POLAR UNTUK MASING-MASING SUMBU
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Cari kuadrat untuk tiap sumbu
𝒔𝒆𝒅𝒆𝒓𝒉𝒂𝒏𝒂𝒌𝒂𝒏 !
UNTUK Massa 1 (m1)
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Lanjutan...
UNTUK Massa 2 (m2)
Jumlahkan !
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Lanjutan...
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Cari Energi Kinetik dan Potensial
Energi Kinetik:
Subsitusikan dari persamaan sebelumnya. Sehingga:
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Lanjutan...
Aasumsikan jika panjang tali dan tidak berubah, maka , sehingga persamaan akan :
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Lanjutan...
ENERGI POTENSIAL (V)
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CARI FUNGSI LAGRANGE
Fungsi Lagrange
CARI MOMENTUM KONJUGATNYA!
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UNTUK MASSA 1 (m 1)
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UNTUK MASSA 2 (m 2)
�̇�𝟐𝟐=𝑷𝜽𝟐
𝟐−𝟐𝑷 𝜽𝟐𝒎𝟐 𝒍𝟏 𝒍𝟐 �̇�𝟏𝒄𝒐𝒔
(¿𝜽𝟏−𝜽𝟐)+𝒎𝟐𝟐𝒍𝟏
𝟐 𝒍𝟐𝟐𝜽𝟏
𝟐𝒄𝒐𝒔𝟐(𝜽𝟏−𝜽𝟐)𝒎𝟐
𝟐 𝒍𝟐𝟒 ¿
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FUNGSI HAMILTONIAN
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Lanjutan...
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Dengan mengubah bentuk dan ke dalam bentuk momentum, maka
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DERET TAYLOR
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KURUNG POISSON
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Kurung Poisson untuk
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Kurung Poisson untuk
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Kurung Poisson untuk